I've never known (without intentional 'password protection', which is usually completely separate from Windows' own security) everyday USB storage to carry over access-control between machines.
I'd have tried several other things, before automatic disk repair, because it's as likely to have made it "work" for the new machine (but everything looks corrupted), whilst breaking whatever effortless access the original machine had.
Always possible, as I've had happen to me more times than I care to count, that the USB drive fails (sometimes half fails) in such a way that it only reports a fraction of the original available space. If your file (and, most importantly, the FAT/whatever index) is still in the good bit, you're ok (for the moment). But if data and/or allocation info are on the dead 'memory' then it's probably a loss. This is between one device and itself. (The "cannot read" might have cropped up on a different machine, but I'll have taken it back to the original one that was ok with it before, to make sure I'm not trying to fead an ext3-formatted drive on my Win2K machine, for example.)
There are other possible glitches, but I think (by 'repairing' it) you probably somewhat added to the original issue. From long experience, though of course that's with more than a few assumptions as I'm not there to look over your shoulder and be sure(/shown to be wrong) what exact 'fixing' process you went through.
Also what you did to the USB originally. You've generally either to administratively 'adopt' the media into your UAC/whatever that a given host machine (or network) uses, or run the utility that SanDisk/etc leaves as the initial contents of your drive. And, unless you're really sure that you're happy for everything to be accessible only under particular circumstances, I'd suggest not bother with either, don't hold anything on there for longer than you might want to risk its loss[1]. You can always individually protect particular files, in other ways. It might not be globally held under a 128bit-AES 'virtual partition', but that's mostly just a gimmick that (when any corruption occurs) can result in the inability to access absolutely everything.
(There's a Life Advice subforum Generic Computer Help thread, or very similarly named, which this particular cry for help might have fitted into, and might get more help than just this broad assumption of mine. Probably better help,foo. Though of course it's also probably a WTF moment...)
[1] Both loss to you, assuming there aren't still copies on your main system(s), and being lost as in 'found by someone else'.