df.groupby(group_keys=True) sometimes doesn't do anything
According to the df.groupby docstring :
```
group_keys : bool, default True
    When calling apply, add group keys to index to identify pieces.
```
But it seems to work for some cases and not others:

```
df = pd.DataFrame({'key': [1, 1, 1, 2, 2, 2, 3, 3, 3],
                        'value': range(9)})

df.groupby('key', group_keys=True).apply(lambda x: x.key)  # index by groups 
df.groupby('key', group_keys=True).apply(pd.np.sum) # index by groups
df.groupby('key', group_keys=True).apply(lambda x: x[:].key) # index by groups
df.groupby('key', group_keys=True).apply(lambda x:x-x.mean()) # does nothing
df.groupby('key', group_keys=True).apply(lambda x:x) # does nothing
```

For example, the following gives the same output regardles of the `group_keys` value
```
import pandas as pd
df=pd.DataFrame(dict(price=[10,10,20,20,30,30],color=[10,10,20,20,30,30],cost=(100,200,300,400,500,600)))
df.groupby(['price'],group_keys=False).apply(lambda x:x)
# result
   price  color  cost
0     13     11   101
1     11     11   201
2     22     21   301
3     21     21   401
4     32     31   501
5     31     31   601

df.groupby(['price'],group_keys=True).apply(lambda x:x)
# same result
   price  color  cost
0     13     11   101
1     11     11   201
2     22     21   301
3     21     21   401
4     32     31   501
5     31     31   601
```
 
xref #22545 for related groupby confusion.

 
