I understand the people who were against using whatever break-through material they were trying to use for the hydrogen tanks claim regular materials would have done the job.
Of course, that's talking while during the design board stage - I'm pretty sure the people working in the actual tried (and failed) hydrogen tanks claimed the same about their design.
It's an engineering question, which I'm not qualified to answer. I think the fact that none tried again by using the supposed regular materials for the hydrogen tanks means the hydrogen tank problem isn't solvable with currently known materials.
Yes it is. A large number of rockets, including the Japanese H-II, the European Ariane 5, the (at the time) United States Space Shuttle, and (later) the Delta IV utilize hydrogen fuel. None of them have any particular problems with their hydrogen tanks, above and beyond the problems inherent to hydrogen (hydrogen brittling, having to manage deep cryogens, and so on). This experience, dating back forty years or so (at the time) was the basis of people saying that tanks made out of conventional materials, which had been proven on a large number of past rockets, would not have been any heavier than the experimental composite tanks that were built. Additionally, as the article posted by e of pi mentions, they began fabricating a conventional hydrogen tank for the X-33, which was lighter than the composite tank, but were prevented from testing it due to the program being cancelled.
The thing about the hydrogen tanks being used in the X-33 design was that they were a new, experimental design made out of a new, experimental composite material, which was made out to be necessary to reach the performance targets e of pi mentions. People pointed out that the technical details of the X-33 design (mainly its lifting body shape) meant that the composite tanks weren't actually any lighter, but that wasn't actually why it was cancelled; it was cancelled due to being tied up in presidential politics. Basically, the whole program was Gore's baby, so when Bush came in instead, it was cancelled. Many of the technical problems with the design were either solvable or avoidable, and the X-33 probably could have flown in some fashion eventually, though as e of pi points out it wouldn't have been nearly as interesting as it was made out to be early on. The whole program was overambitious from the beginning, really.