There is a kind of superstition in DNA fora wich contists in matching a single hg with a certain ethnolinguistic group, as if a monoparental mutation carried the language gen.
In these days it's obvious that is wrong, but many people assume it was certain in the past, a few thousands of years past. We can imagine isolated populations, diseases and other epysodes, but humans mixed yesterday as today do.
Saying that first IE speakers carried only one Y-DNA hg is highly speculative. Even if they carried mostly a single hg, we wouldn't know who were the true "intruders" of IE languages. In the same way, we could say that this/these hg's could be present in the ethnogenesis of other linguistic groups.
I certainly won't discount the idea that the populations back then were admixed, probably to a large degree, especially where IE originated and there were a lot of peoples of different origins crossing paths. One phenomenon we do see is that genetic drift seems to have occurred, for whatever reason, faster on Y-DNA than on mtDNA historically. Another is that culture and language seems to generally stick with Y-DNA closer than with mtDNA. The result is that Y-DNA seems to more commonly have a one-to-one correspondence with language groups than mtDNA, and so we often speak of a haplogroup as having a language or vice-versa, even when that is obviously not the case.
Say a language family is observed nowadays as being spoken by people with unrelated haplogroups A and Z. We may postulate that the original haplogroup was A, and consider ourselves to be right if the original population was admixed with A, B, and C, or wrong if it was in fact X, Y, and Z. If the original populations was admixed with A and Z, then we would be wrong in postulating that EITHER was the original. Same for if the original population was D and E... although then we could still try to find whether A or Z was the first to join the population.
In the case of IE, I think that assuming that neither was the original and it originated with both of them to be a bad assumption... the spread of R1b doesn't seem to partner well enough with R1a, and there are non-IE R1 subclades that make me hesitant to assume that R1a and R1b stayed together as a population. All said, I could be very wrong.
If we take a sight at the Y-hg's tree we can observe that R is closer to Q than it is to I or J, but autosomal DNA says that most of R carriers match better with I and J ones than with Q's. It would be highly speculative to say that R's couldn't be IE's because most of Q's carriers speak a language that differs from R's carriers ones more that the latter do with I's or J's ones. You won't find too much people who buy this speculation, it seems that some "cheap" ideas are more healthy than others.
Obviously, Y-DNA haplogroup - autosomal DNA correspondence tends to be poor. Also, I get your point, but R/Q is a bad example because their split is, I think, older than what we would expect the age of a language family to be.