Hi, Jessica! The good news is that your brother's R-Z28496 (also known as FGC22592) designation is very likely to be completely accurate. The also good news is that if you have a genealogical hypothesis that a male in your tree does not match the hierarchy down to R-Z28496 (which, working its way upward, would be < FGC22940 < Z142/S11 < Z49 < L2/S139 < U152/S28 < P312 < L151 < P310 < L51 < L23 < M269) then--ta dah!--the hypothesis is correct. But the bad news is that R-Z28496 probably branched off from FGC22940 over 2,000 years ago, maybe as long as 4,000 years if guestimating from Yfull.com.
With close to 200,000 yDNA defining SNPs (single nucleotide polymorphisms) identified, and many of those added to the taxonomy just in the past several years, yDNA haplogroups can get a little...complicated. Unless a haplogroup designation--as specified by a particular SNP--is one that only recently arose (and these are almost always identified only by full-sequence Y-chromosome testing like FTDNA's Big Y-500) it really isn't useful as positive evidence for genealogy. It can be great at disproving a relationship, and it can also provide clues for continued searching, but there's no "matching" involved at that level.
The typical yDNA tests at FTDNA look at STRs, short tandem repeats, and don't test SNPs at all. These are like copy machine stutters where the same sequence of a few alleles get repeated several times. Unlike a polymorphism, these happen much more frequently and the differences--or similarities--between values can put things squarely in the genealogical timeframe. These STR tests (you'll see them called Y-37, Y-67, and Y-111 tests) don't actually examine any SNPs at all. They predict a haplogroup based on the results of the STR values.
Companies like 23andMe and Living DNA don't do specific yDNA or mtDNA tests like FTDNA, YSEQ, and others do. The marketing is a tad misleading when they say, for example, that they perform three tests. It's all one test using what's called a microarray BeadChip that's partially customizable. The test looks only at SNPs, not at STRs, and the SNPs are targeted by the way the chip is programmed (has to do with the way nucleic acids bond selectively with one another). Some of the chip's programming targets SNPs in the Y-chromosome.
Voila! That's how an autosomal DNA test can accurately return a yDNA (and mtDNA) haplogroup. However, it's all about the programming. The chip can look only at what it's programmed to look at, so the haplogroup can only be defined to the extent of that programming. Where the Big Y test tries to look at as many of the Y-chromosome's 58 million base pairs as possible and can find novel or unique SNPs that might just this generation be splitting off on their own, the chip-based test can only look at the few thousand base pairs it's programmed to locate. But as far as it goes, it's quite accurate.
Your brother, as am I, is among one of the most common yDNA subclades in the world, R-M269. That's why 23andMe returned a fairly deep result for him: programming the microarray chip to look levels deep in M269 makes numbers sense. Others who are in less common haplogroups will see results only at a higher level. As an example, a man in haplogroup E might get a result that shows E-M44, which is equivalent to E1a1, only three levels deep in the E phylotree.
P.S. Good on ya getting your parents and a grandmother tested early. So many folks taking autosomal tests right now start out interested only in the ethnicity/admixture, and only later come to understand how irreplaceable to genealogy are results from earlier generations.