Spurious: Not genuine. Counterfeit.  Believable, but false. 

This word started out in Latin as spurius, meaning “illegitimate.”  It was even sometimes used as a first name among the Romans for a child born out of wedlock.  

These days, we still use the word to describe something illegitimate.  But, we mostly use it to describe something false.

For example: I’ve lived long enough to know I cannot trust the spurious promises of politicians.