How do they have a smaller budget? Its AMD, they recently got that massive payoff from intel to drop the antitrust lawsuit, if anything its nvidia with the smaller budget.
I gather they pulled it off by testing out TSMC's 40nm process with their old 4770 cards rather than chance it with a brand new series, so they used the 4770 to get the kinks worked out so everything would be smooth for the 5xxx cypress cores.
AMD have a larger budget, but budget is largely determined by size of teams, if you won the lottery tomorrow, you'd still be living in the same house, have the same car and the same computer, over a short space of time you'd likely buy a new house, but finding the right house takes time no matter how much money you have.
CPU cycles are determined in lengths of years, or even half a decade from early design to out in retail, GPU cycles are shorter but the team that started the 5xxx series cards aren't the "uber rich we have so much money its embarassing" R&D team that Intel and Nvidia had, not by a LONG LONG shot.
Even then, just because you have large backers, these aren't the Chelsea owners, Abu Dhabi's business success is not throwing money around, its being very very good at what they do.
Theres no need to spend 1billion more just because you can, in other words, they can afford to employ everyone at AMD, Intel, Nvidia, IBM, Samsung and anyone else all together from the change in one of their pockets, the problem being those people have jobs, they don't need that many people, and finding the best people takes time. I'm fairly sure investment and R&D spending will increase, quite a lot, but also factor in very very few companies massively increase spending when the world economy is crashing badly.
Either way you have the reason for the success partially right, they learnt a LOT form the 4770, but not quite as much as you think. They learned that via's weren't being reproduced accurately so large redundancy will help MASSIVELY, and that transistor size is simply not remotely accurate.
But the fundamental reason they weren't effected is down to trial and error. They built the 2900XT on the basis of TSMC's promises, post 2900XT they decided to build a core that would still work in the case that TSMC screw up, because when you assume they'll screw up you won't be screwed yourself.
The way to protect yourself from bad and leaky processes is to make smaller more efficient cores, with lower clock speeds and higher IPC. Sound familiar? Yes every other chip maker in the world follows the idea that Ghz is an old idea. Intel's chips are smaller than AMD's, and more efficient, how does AMD compete, on price. Nvidia ignore the trend of every other chip maker on the planet, and decide not to compete on price either, they are flat out stupid.
Nvidia have been trying to make 40nm chips for well over a year now, from failed designs of the gt200b they should have known how to "fix" Fermi, they just wouldn't. The 3 respins still haven't fixed the fundamental issues.
THe problem is, its almost a certainly that Nvidia will make a pretty huge loss on every single sale of a 470/480gtx, and thats just not good business.
But as others have listed, we tend to enjoy it when arrogant, rude, cheating companies screw up, we all like a little karma, makes us feel better about life and the fairness of it all I guess, it doesn't matter the company or area, we all get tickled when a "mean" company gets screwed and we all love the underdog.
AMD's 5xxx series only looks so fantastic due to Nvidia's screwups, in reality its a pretty simple die shrink + increase in shaders compared ot the 4870 series, which was a great core but also a fairly simple idea. THe 2900xt is technologically, well, it had so many fantastic breakthroughs all in one card. Tesselation dx10(10.1, I'm not actually sure, I think it is dx10.1 but dx10.1 simply wasn't out back then), ringbus memory(total overkill but fantastic tech), it came with the new shader style which was a monumental change in shader style, pretty much an unmatched change in terms of graphics technology since I can remember being into computers(GF3 ish era).
THe 5xxx series is still at its heart a 2900xt, cut down for the better of the consumer, costs and manufacturing but still fantastic.
Also when you consider where the 5xxx stems from, the 2900xt and the massive changes in the 3870, you'll realise those were during the "lean" Ati/AMD years.