I've been on FB for a few years and never get any weird messages except the occasional "reminder someone has invited you to FB (when they're already on my list)"
I think it's from FB, scanning our email addresses and making sure that we get as many friends added as possible" (a bit of a glitch, I think).
But to be quite honest with you (and I'm someone who rarely jump to conclusion, but tries to give people the benefit of the doubt). But this spam you mention is very UNLIKELY. I equate it to when you see a transaction you don't recognize in your bank account and think, "could it be fraud?" Well, the chances are VERY SLIM to NONE that there's a fraudulent transaction, and you just don't recall what the purchase was for.
And you have to know your husband too. Because if it was on my husband's email, I would have to say that I would believe my husband because I really know him and what kind of person he is. But if you don't know whether to believe him or not and are on this site to help investigate then that's something you need to consider.
Btw, my husband never gets any emails from FB that's not legitmate.
Maybe you can try to change the privacy to make it strictly friends only. That should at least stop any illegitimate emails if that really is the case, and he's telling the truth.
good luck.