But I have to question, why should a DM buy a book that's about player options? Why should he be the one spending the money, when it's 1) the players using it, and 2) the only reason the DM has it is to check the rules?
Speaking only for myself:
I expect to be able to check up on PC capabilities, and often have to do such things between sessions. If the player were willing to leave his copy with me for the duration of the campaign (or, I suppose, were there an electronic version I could reference), that would be fine, but otherwise, I need my own copy.
Do you think DMs should be the ones buying the splats?
No. But then, it has been my experience that most games play better in a core-rules-only manner anyway, or perhaps with a very small set of carefully selected supplements. Too many games have later supplements that introduce poorly balanced elements (due to poor playtesting), power creep (again, playtesting... or deliberately), or just add complexity where it isn't needed.
4e appears to be a bit better in this regard, in that the creeping errata take care of most of the balance issues. But then, I don't run 4e... and in part this is because I'm turned away by option bloat.
Does a DM have to own the book for it to be allowed in the group? I know that this is how quite a few Dms operate (if I don't own it you can't use it), but that 1) assumes the DM reads the entire thing and knows all the broken bits anyways, 2) puts the purchasing burden on the DM.
I take that view. In fact, I go further: at the start of the campaign I identify the books that will be used (and sometimes, the parts of books that will be used), and after that the list is fixed. We don't change the rules mid-stream.
There are two reasons for this. The first is because of balance issues, as I've mentioned above. The second, however, is that I insist on a level playing field for all participants. If Al gets to use a particular sourcebook, so does Bob. And while, in theory, they could share Al's copy, that has several practical issues (notably Bob's ability to check the book between sessions). Limiting it to only books I own at least guarantees everyone reasonable access to the books, and ensures that I can check the books between sessions.
As for the purchasing burden... I've spent way more on RPGs than I probably should. Traditionally, it's never been a problem - for the games I've been running, I've typically owned way more books than any of the players, and usually more than all of them combined.