I have all the respect in the world for people at respectable TB rescue organizations (like the ones you mentioned) who work so hard to re-home/rescue TBs. Naturally, these organizations rely on the support of good horsemen/women with a penchance for OTTBs to function. But, I know firsthand that a fair number these situations do not work out (even when the adopters have the best of intentions). You would not be doing anyone any favors if you have to return a horse--least of all yourself.
I should also note that while while no horse in a reputable rescue organization should be suffering due to a lack of veterinary care, most rescues do not have the resources to treat their horses for low-level chronic conditions like ulcers, skeletomuscular issues, underlying hoof problems, etc. And you can pretty much bet that if you're purchasing an OTTB that your horse is going to have some, if not all of those problems...As I noted in an earlier post, there are exceptions to the rule, but realistically you should bank on spending a good chunk of change on your horse before you can start training/riding.
In view of that consideration, if one of your main interests in purchasing a OTTB is because they strike you as talented, inexpensive horses, now is a good time to walk away. Yes, there are OTTBs out there who are and always will be sound, sane, and healthy, with nothing more than a couple of flakes of hay a day, no shoes, and one ride a week. But don't be lured by the siren song-- I can't tell you how many people I met who were just thrilled with their new $400 equine partner-- after a few months, and a few thousand $, their smiles didn't shine quite so brightly.