The traditional analysis is fine. The "traditional" analysis is, if it is explained correctly, an approximation; it's based on calculating the expected number of cells that are 0/1 when you hash the keys into the filter, and then analyzing as though that was the actual number. The point is that the number of cells that are 0 (or 1) are tightly concentrated around their expectation, so it's a fine approximation. This was well known, and can be found, I think, even back in my survey article with Andrei Broder.
This paper says that really the performance of a Bloom filter is a random variable (corresponding to the actual fraction of 0/1 entries), and if you want to calculate that performance exactly for some reason, you need to do the combinatorics. For smaller filters, you'll see an arguably non-trivial difference.
I've talked with the authors of this paper. Their analysis is all well and good (though I'd argue that it isn't deep or new); their motivation that the "traditional analysis is wrong" was, I think, exaggerated.