Inconsistent index in result of groupby apply 
### I'm not really sure if this is an "issue" or the intended behavior, but it just seems unnatural to me to get this result.

```python
import pandas as pd

df = pd.DataFrame({
    'a': [1, 1, 2, 2],
    'b': [3, 3, 4, 5],
})
df

   a  b
0  1  3
1  1  3
2  2  4
3  2  5
```
```python
df1 = df.groupby('a').apply(lambda x: x)
df1

   a  b
0  1  3
1  1  3
2  2  4
3  2  5
```
```python
df2 = df.groupby('a').apply(lambda x: x.copy())
df2

     a  b
a
1 0  1  3
  1  1  3
2 2  2  4
  3  2  5
```
Notice that the two produces different results.
A simple code trace tells me this difference comes from `BaseGrouper.apply` which return `mutated=False` for `.apply(lambda x: x)` and `mutate=True` for `.apply(lambda x: x.copy())`

This could cause unwanted result when we try to concatenate them.
```python
pd.concat([df1, df2])

        a  b
0       1  3
1       1  3
2       2  4
3       2  5
(1, 0)  1  3
(1, 1)  1  3
(2, 2)  2  4
(2, 3)  2  5
```

Good thing is, the `apply` method is able to handle this concatenation automatically.
```python
def func(data):
    if 1 in data['a'].values:
        return data
    else:
        return data.copy()

df.groupby('a').apply(func)

   a  b
0  1  3
1  1  3
2  2  4
3  2  5
```


#### Output of ``pd.show_versions()``

<details>

[paste the output of ``pd.show_versions()`` here below this line]
INSTALLED VERSIONS
------------------
commit           : None
python           : 3.7.3.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : None.None

pandas           : 0.25.3
numpy            : 1.17.4
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 19.3.1
setuptools       : 42.0.2.post20191203
Cython           : 0.29.14
pytest           : 5.3.2
hypothesis       : 4.44.2
sphinx           : 2.3.0
blosc            : None
feather          : None
xlsxwriter       : 1.2.6
lxml.etree       : 4.4.2
html5lib         : 1.0.1
pymysql          : None
psycopg2         : None
jinja2           : 2.10.3
IPython          : 7.10.2
pandas_datareader: None
bs4              : 4.8.1
bottleneck       : 1.3.1
fastparquet      : None
gcsfs            : None
lxml.etree       : 4.4.2
matplotlib       : 3.1.1
numexpr          : 2.7.0
odfpy            : None
openpyxl         : 3.0.2
pandas_gbq       : None
pyarrow          : None
pytables         : None
s3fs             : None
scipy            : 1.3.2
sqlalchemy       : 1.3.11
tables           : 3.6.1
xarray           : None
xlrd             : 1.2.0
xlwt             : 1.3.0
xlsxwriter       : 1.2.6
</details>
