diff --git a/dvc/config.py b/dvc/config.py
--- a/dvc/config.py
+++ b/dvc/config.py
@@ -232,8 +232,10 @@ class Config(dict):
     CONFIG_LOCAL = "config.local"
 
     def __init__(
-        self, dvc_dir=None, validate=True
+        self, dvc_dir=None, validate=True, tree=None,
     ):  # pylint: disable=super-init-not-called
+        from dvc.scm.tree import WorkingTree
+
         self.dvc_dir = dvc_dir
 
         if not dvc_dir:
@@ -246,6 +248,9 @@ def __init__(
         else:
             self.dvc_dir = os.path.abspath(os.path.realpath(dvc_dir))
 
+        self.wtree = WorkingTree(self.dvc_dir)
+        self.tree = tree.tree if tree else self.wtree
+
         self.load(validate=validate)
 
     @classmethod
@@ -304,8 +309,32 @@ def load(self, validate=True):
         if not self["cache"].get("dir") and self.dvc_dir:
             self["cache"]["dir"] = os.path.join(self.dvc_dir, "cache")
 
+    def _load_config(self, level):
+        filename = self.files[level]
+        tree = self.tree if level == "repo" else self.wtree
+
+        if tree.exists(filename):
+            with tree.open(filename) as fobj:
+                conf_obj = configobj.ConfigObj(fobj)
+        else:
+            conf_obj = configobj.ConfigObj()
+        return _parse_remotes(_lower_keys(conf_obj.dict()))
+
+    def _save_config(self, level, conf_dict):
+        filename = self.files[level]
+        tree = self.tree if level == "repo" else self.wtree
+
+        logger.debug(f"Writing '{filename}'.")
+
+        tree.makedirs(os.path.dirname(filename), exist_ok=True)
+
+        config = configobj.ConfigObj(_pack_remotes(conf_dict))
+        with tree.open(filename, "wb") as fobj:
+            config.write(fobj)
+        config.filename = filename
+
     def load_one(self, level):
-        conf = _load_config(self.files[level])
+        conf = self._load_config(level)
         conf = self._load_paths(conf, self.files[level])
 
         # Auto-verify sections
@@ -375,7 +404,7 @@ def edit(self, level="repo"):
         _merge(merged_conf, conf)
         self.validate(merged_conf)
 
-        _save_config(self.files[level], conf)
+        self._save_config(level, conf)
         self.load()
 
     @staticmethod
@@ -386,20 +415,6 @@ def validate(data):
             raise ConfigError(str(exc)) from None
 
 
-def _load_config(filename):
-    conf_obj = configobj.ConfigObj(filename)
-    return _parse_remotes(_lower_keys(conf_obj.dict()))
-
-
-def _save_config(filename, conf_dict):
-    logger.debug(f"Writing '{filename}'.")
-    os.makedirs(os.path.dirname(filename), exist_ok=True)
-
-    config = configobj.ConfigObj(_pack_remotes(conf_dict))
-    config.filename = filename
-    config.write()
-
-
 def _parse_remotes(conf):
     result = {"remote": {}}
 
diff --git a/dvc/ignore.py b/dvc/ignore.py
--- a/dvc/ignore.py
+++ b/dvc/ignore.py
@@ -254,3 +254,6 @@ def stat(self, path):
     @property
     def hash_jobs(self):
         return self.tree.hash_jobs
+
+    def makedirs(self, path, mode=0o777, exist_ok=True):
+        self.tree.makedirs(path, mode=mode, exist_ok=exist_ok)
diff --git a/dvc/repo/__init__.py b/dvc/repo/__init__.py
--- a/dvc/repo/__init__.py
+++ b/dvc/repo/__init__.py
@@ -91,14 +91,14 @@ def __init__(self, root_dir=None, scm=None, rev=None):
         else:
             root_dir = self.find_root(root_dir)
             self.root_dir = os.path.abspath(os.path.realpath(root_dir))
+            self.tree = WorkingTree(self.root_dir)
 
         self.dvc_dir = os.path.join(self.root_dir, self.DVC_DIR)
-        self.config = Config(self.dvc_dir)
+        self.config = Config(self.dvc_dir, tree=self.tree)
 
         if not scm:
             no_scm = self.config["core"].get("no_scm", False)
             self.scm = SCM(self.root_dir, no_scm=no_scm)
-            self.tree = WorkingTree(self.root_dir)
 
         self.tmp_dir = os.path.join(self.dvc_dir, "tmp")
         self.index_dir = os.path.join(self.tmp_dir, "index")
diff --git a/dvc/repo/tree.py b/dvc/repo/tree.py
--- a/dvc/repo/tree.py
+++ b/dvc/repo/tree.py
@@ -12,7 +12,7 @@
 logger = logging.getLogger(__name__)
 
 
-class DvcTree(BaseTree):
+class DvcTree(BaseTree):  # pylint:disable=abstract-method
     """DVC repo tree.
 
     Args:
@@ -236,7 +236,7 @@ def get_file_hash(self, path_info):
         return out.checksum
 
 
-class RepoTree(BaseTree):
+class RepoTree(BaseTree):  # pylint:disable=abstract-method
     """DVC + git-tracked files tree.
 
     Args:
diff --git a/dvc/scm/git/tree.py b/dvc/scm/git/tree.py
--- a/dvc/scm/git/tree.py
+++ b/dvc/scm/git/tree.py
@@ -19,7 +19,7 @@ def _item_basename(item):
     return os.path.basename(item.path)
 
 
-class GitTree(BaseTree):
+class GitTree(BaseTree):  # pylint:disable=abstract-method
     """Proxies the repo file access methods to Git objects"""
 
     def __init__(self, git, rev):
diff --git a/dvc/scm/tree.py b/dvc/scm/tree.py
--- a/dvc/scm/tree.py
+++ b/dvc/scm/tree.py
@@ -37,6 +37,9 @@ def walk_files(self, top):
                 # NOTE: os.path.join is ~5.5 times slower
                 yield f"{root}{os.sep}{file}"
 
+    def makedirs(self, path, mode=0o777, exist_ok=True):
+        raise NotImplementedError
+
 
 class WorkingTree(BaseTree):
     """Proxies the repo file access methods to working tree files"""
@@ -90,6 +93,9 @@ def stat(path):
     def hash_jobs(self):
         return max(1, min(4, cpu_count() // 2))
 
+    def makedirs(self, path, mode=0o777, exist_ok=True):
+        os.makedirs(path, mode=mode, exist_ok=exist_ok)
+
 
 def is_working_tree(tree):
     return isinstance(tree, WorkingTree) or isinstance(

For the record: the issue is that in external repo we operate on virtual trees(we don't checkout to the branch), but we still read config through regular open() calls, which is causing this issue. Need to make our config use repo's `self.tree` to read/write configs.
diff --git a/tests/unit/repo/test_repo.py b/tests/unit/repo/test_repo.py
--- a/tests/unit/repo/test_repo.py
+++ b/tests/unit/repo/test_repo.py
@@ -3,7 +3,8 @@
 import pytest
 from funcy import raiser
 
-from dvc.repo import locked
+from dvc.repo import NotDvcRepoError, Repo, locked
+from dvc.utils.fs import remove
 
 
 def test_is_dvc_internal(dvc):
@@ -127,3 +128,27 @@ def test_skip_graph_checks(tmp_dir, dvc, mocker, run_copy):
     dvc.add("quux")
     run_copy("quux", "quuz", single_stage=True)
     assert mock_collect_graph.called
+
+
+def test_branch_config(tmp_dir, scm):
+    tmp_dir.scm_gen("foo", "foo", commit="init")
+
+    scm.checkout("branch", create_new=True)
+    dvc = Repo.init()
+    with dvc.config.edit() as conf:
+        conf["remote"]["branch"] = {"url": "/some/path"}
+    scm.add([".dvc"])
+    scm.commit("init dvc")
+    scm.checkout("master")
+
+    remove(".dvc")
+
+    # sanity check
+    with pytest.raises(NotDvcRepoError):
+        Repo()
+
+    with pytest.raises(NotDvcRepoError):
+        Repo(scm=scm, rev="master")
+
+    dvc = Repo(scm=scm, rev="branch")
+    assert dvc.config["remote"]["branch"]["url"] == "/some/path"

dvc get --rev doesn't work if master is not a dvc repo
## Bug Report

### Please provide information about your setup

**Output of `dvc version`:**

```console
DVC version: 1.1.7
Python version: 3.7.2
Platform: Darwin-18.7.0-x86_64-i386-64bit
Binary: False
Package: pip
Supported remotes: http, https, s3
Cache: reflink - supported, hardlink - supported, symlink - supported
Repo: dvc, git
```

**Additional Information (if any):**

Discord link with all info

https://discordapp.com/channels/485586884165107732/485596304961962003/731227119954427904


tests/unit/repo/test_repo.py::test_branch_config
tests/unit/repo/test_repo.py::test_skip_graph_checks tests/unit/repo/test_repo.py::test_is_dvc_internal tests/unit/repo/test_repo.py::test_locked