They do, especially those of our kind (read: internationals) who are minted like heck (because of Eastside and Southside, ehe. I definitely don't fall under that category.) It's just that after the close-to-campus halls, the *somewhat* next in line (maybe even on par) on the "oversubscribed" list would have to be cheap singles (you'd be surprised about how many hate the idea of sharing.)
Apart from the halls, also try not to get too attached to the thing about having your own fridge. Not many halls offer them (there's another hall that does but I forgot which), and most of us "normal" folk do without it anyway. It's not a "really need" (your words, not mine...!) thing, unless you're a diabetic - in which case, you can email them and they will provide you with a fridge for your insulin.
Also, most of them have pool tables (some free, some maybe 20p or so a go) and there are quite a few good practice rooms in the Blyth Center on campus + pianos in some of the other halls, so it's not like Wilson is the only one that has all you need (yay for compromise.
) It's just a matter of having a mature enough mindset to make do with/appreciate what you get given.
What other halls have you applied for (or if you haven't sent off your app, are considering?) Based on the fact that you prioritized price, I'm guessing that you'd have gone for the other cheaper singles, which would be the Evelyn Gardens ones...
PS// I'm assuming you'll be under 18 in Oct...otherwise, that single-room guarantee won't happen. Some of the under-18s I spoke to were only allowed to put down one option on the form, which was weird.