My wife assures me I gave her an std, but I never had symptoms. Is she lying?

Complicated. First, you would need to know what kind of std she has, what are or were the symptoms, are there cultures, are you both monogamous, etc. There are many variables to your questions. Technically, there are indeed some conditions that are considered std's which could be transmitted even if you thought you never had them. You should both see an md...Together.
Who knows... Not sure about lying, etc... But it certainly is possible you had an std and didnt have any symptoms. In fact, its quite common to have gonorrhea and/or chlamydia, and even herpes or hpv and not have any symptoms. Same for hiv. So this is possible. However, its also possible she got the std from someone else.