This reverts commit 4023228.

We use sys.exit. On purpose.
We should therefore not be catching SystemExit.

This is probably wrong. But less wrong than handling *all*
BaseException. Reports of this happening may be the result of
 some *other* async Timeout in the wsgi app bubbling through to us.

Gevent docs promise:
"[..] if *exception* is the literal ``False``, the timeout is still raised,
   but the context manager suppresses it, so
   the code outside the with-block won't see it."

There is not need to excessively produce high-severity logs, while
there are ways to reach that point from entirely benign network errors.

This partially reverts commit 0b10cba.