Tool: Pyflakes
Processed Files:
    reviewboard/reviews/models/review_request.py

Ignored Files:
    reviewboard/templates/reviews/review_detail.html



Tool: PEP8 Style Checker
Processed Files:
    reviewboard/reviews/models/review_request.py

Ignored Files:
    reviewboard/templates/reviews/review_detail.html

 undefined name 'silent'

Col: 9
 E303 too many blank lines (2)

Typo: "reviewers" should be "reviewer's".

You don't really need this condition. If groups is empty, then Python will automatically avoid entering the body of the for loop.

We usually surround our strings with single-quotes instead of double-quotes.

Single-quotes, not double-quotes.

Consider replacing this with:
return not self.is_private()

Make this into a @property.

This is missing a "Returns" section. It should be like:

"""

...

Returns:
    bool:
    <description of the return type>
"""

The return is a conclusion. A new paragraph. It should have a blank line before it.

<li> is not allowed in a <span>. It needs to be the other way around.

The design for this is going to need to change. It's not enough to stick the private flag in extra_data, because we can't query on it, and it's crucial that we can query on it, since otherwise private review requests will show up in the dashboard, All Review Requests page, search, etc.
You'll need to make a new private field on the model.
You'll also need to update the _query function in reviewboard/reviews/managers.py (see the if filter_private section) to consider this field.