Boy, this is a tough one. In my opinion, there's fault at both ends of this. I think you're correct in that the cake was probably cold and that's why it tasted dry and the "shortening" comment probably comes from the "mouthfeel" of IMBC not necessarily the taste -- have you ever put cold IMBC in your mouth? It is similar to the feeling of putting a cold pat of butter in your mouth - nasty! once it melts it tastes fine, but the initial shock can be a bit disheartening if you're not familiar with it and the closest thing people can relate it to is shortening because that's what they assume all icing is made out of.
You may have given them step but step instructions and the maybe the followed them and maybe they didn't but, from personal experience, there is no way the middle of three tier cake will come to "room temp" in 30 to 60 minutes. I've cut into cakes that were refridgerated overnight and had been out for 4 hours and was shocked to find the centers of the stacked tiers (particularly the larger bottom ones) to still be cold and the filling solid.
So even though you were "c.y.a" but giving specific instructions, it still may not have been enough, especially for someone with no cake experience. Unfortunately, your only real fault here is the lack of a contract. By listing specific terms i.e. they assume all respsonsibility for the condition of the cake, etc. once it leave your premises if it is picked up and issues as far as quality, etc. must be reported withing 24 hours, etc. etc and having them sign off of this, it releases you from these type of incedents (or at least gives you a leg to stand on).
Unfortunately, I'm not sure how I would proceed in this situation either. It sounds like you're confident in the quality of your product so I guess I would say stand behind it. At this point I wouldn't be comfortable in tasting the leftovers, as other posters of said, who knows what they've done to it. I would email her (for paper trails sake and you can follow up with a phone call) and explain that you've thought it over and unfortunately due to the time that has elapsed, etc. that tasting it at this point would be moot. Then kindly explain to her all that you've already expressed here regarding your cake and never having a complaint about it before, etc.
Although you could offer her a free anniversary cake, I wouldn't think that someone that's not happy with how your cake tasted would really want another one. Maybe a small refund or nothing at all. It sounds like no matter what you do, she's not going to be happy (well, unless she get's her money back, lol!)