Good question, Jonathan. I would think, off the top of my head that you'd probably have a better chance of this occurring (passing through refresh rates) with a more expensive box rather than the bargain solution - but I'm not sure. There has to be a reason (other than greed) for some manufacturers charging more for one product over a similar one.
I will say that your question points out why I think that it is so important to try to get permission to return a product to a vendor at no charge (other than postage, etc.) if it doesn't do the job for you. And don't think I'm just trying to steer you to the the more expensive products. I still advocate starting with the least expensive option and working your way up if something doesn't fit.
Incidentally - when I posted the article last night the HTF was undergoing some scheduled maintenance (I think) so things were running really slow. I intend to try to get Jano Banks (The HDMI guy) on board as soon as we get him set up so that he can answer questions just like the one you just posed. Jano would probably know as well as anyone what signals get through an HDMI path unscathed and which do not. He's a very busy man, but he said he will try to check in from time to time to provide answers to HDMI issues. Just don't expect quick turnaround, especially since I don't speak for him.
Happy Handshaking!