I don’t agree with this sentiment… How I view it is, as others have said, to perhaps downplay it or just mention it casually (like you said in the first post). If you tell them it’s one thing (like “action”) then they might resent it for having experienced it a different way. @Kanon mentioned something to that effect in the Hibiki no Mahou / Hibiki’s Magic General Discussion thread. (He went into the story expecting it to be something different than what it was. He had to adjust his expectation to enjoy it.) I have had similar experiences as well, though I don’t recall specifics.
Now, as for how I invite people to watch Key shows (or read the VNs) I haven’t done that recently. My first attempt was I gave a recommendation to a friend and mentioned “This was the first thing I’ve watched that actually made me cry,” to which he showed intrigue and asked about the show. However, I didn’t get the impression he would actively watch it (rather, I felt it would be a passively watched thing where specific moments would be missed and he just wouldn’t care in general, if he even watched it at all). So after that I mentioned “Actually, you probably shouldn’t watch it. I don’t think it’s the type of show you’d like.” The person in question isn’t a fan of anime, and Clannad isn’t a good gateway for someone into survival/documentary-type stuff like he is. I figure that if he ends up liking anime that maybe he’d find it on his own.
On the other hand, I shipped a set of games and DVDs to a friend who is a fan of anime. It contained some Key stuff (Air, Kanon), but also a few other things. This person is usually busy, so I have no idea when they’ll get to it. They did say they were interested though. (However I think that’s just a passive interest.)
As for whether I care, I think I care too much when it comes to these things. The stories themselves I’ve grown incredibly attached to. If I recommend that story, this thing that has (in a way) become a part of myself, to someone else and they don’t like it? Then, even though I consciously don’t care, subconsciously (as all humans do) there’s that crave for validation, and their negative reaction will make a stab at it. If someone I don’t know is dismissive of those stories, then I don’t care. If someone I personally know says something bad about them, then I also don’t care that much. But it would still bother me.