"Its illegal to grant CPT before the first year of fulltime enrollment" - (Unless rules have changed recetly) this piece of information is absolutely incorrect. CPT has nothing to do with USCIS or any other governmental bodies that handles employment authorization. CPT rules varies greatly with universities.

The main point here we are missing is that - 'that shady university in CA' was opened by some indians and chinese, primarly focusing for those students who alreday have masters degree and needed some extra time or way of finding jobs whiling just maitiang F1-status. If you are excepting a degree from that college and applying for a job with that degree, then its ur mistake that you got into something without knowing anything.