well, thanks again to the others who have responded. and thanks for the really nice comments about my DH. he really is a gem.
of course my initial response was "what the h*ll did you say to her to encourage this??" he assured me that during the 12 class meetings this woman sat next to him once or twice and that he really only chatted with her about aspects of her work that were applicable to the class they were taking and that was about it. part of the class is networking
he is a manager in the hospitality industry and being friendly and open is etched into his very being. on a zillion occasions, i have seen him work a room and have been blown away by his charisma and charm--especially with little old ladies. so i can see where a person who is looking for something or someone might read more into what he perceives as small talk. i told him he should tone it down when dealing with a similar situation and he said he would.
both DH and i have significant trust issues. i have the history with my own father's, um, let's call them "indiscretions," plus a previous long-term relationship that was torn apart by cheating (among other things). my DH was engaged 12 years ago, and with the invitations almost in the mail, his fiancee revealed that she'd been having an affair and they called off the wedding. SO this is something we both feel quite strongly about. i trust him as much as i can possibly trust anyone, and that sadly still isn't 100% due to no fault of his own. but given his openness and communication about this particular woman and her invitations, i have to give him the benefit of the doubt.
ultimately i think there are lonely people out there, and i agree with Alwayslearning that some can be "crafty" and manipulative. i think the woman in our situation was including me in her invitations as a smoke screen like Oriole subtly points out.