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.