Yeah! I solved the problem!
Creating an empty _init_py in the global Lib/site-packages/flaskext next to the babel.py file solves the problem.
Importing Babel from the local environment now works as expected and as it worked in the global environment.
We can use the two forms from flaskext.babel import Babel and from babel.ext.babel import Babel. However the forms *from flask_babel import Babel* or *import flask_babel* don't work.
Note that I'm running on Windows 7 64bit with Python 2.7 in C:\Python27. The absence of init.py file may not be a problem on unix computers.