There is also the fact that everyone knows that Diana doesn't lie, so Tom wouldn't be looking for it.
The only problem would be that I thought one of Tom's functions was as a counterespionage agent, so he'd have to have experience with being a good bullshit detector. But if he's not looking for it, and trusts the person lying to him, and wants what they say to be the truth pretty badly, I can see it going that way as well.