Q. "Obviously most apples tend to be biennial; is this just an extreme example of biennial (not) bearing? (Does this happen - absolutely no blossoms in the "off" years?)"
A. I don't have enough experience with the variety to know if this is common with Brambley but with certain bienniel varieties it is quite common. Here, Goldrush, amongst others, can be like that (Z6, NY), especially if grown on a site with any sun exposure limitation.