First of all, the argument does not "hinge" on them being cousins. The claim is merely that they were not biological children of Mary. One possibility, which seems consistent with the text, is that they were cousins.
It's really beyond dispute that neither Hebrew nor Aramaic have specific terms for cousin or nephew or brother in-law or half-brother That is why Philip the Tetrarch is identified as Herod's "brother" in Scripture, though he was really Herod's half-brother, and why Abraham addresses Lot as "my brother," though the text elsewhere makes it clear that Lot was really his nephew.
I think you need to read Ruth. Ruth is CLEARLY named as Naomi's Daughter -in-law. So, appearently, you are wrong. If the Bible says that they are brothers, then you HAVE to assume they are brothers, UNTIL compelling arguement comes forth that demonstrates otherwise. So far all I have seen is supposition. That won't do.
Abraham called his wife his sister, also, which got him into all sorts of trouble.