Interestingly, in the two versions of Perl that I have access to here, 5.004_04 and 5.6.1, this snippet
outputs bb.$_ = "aa"; $$_ = "bb"; print $aa;
Notice the lack of my, and the lack of use strict; - it only works without strictness, which I guess was the point of the OP's question about turning off strict vars.
It's not a good thing to do, admittedly - though it would seem to be valid syntax, at least historically.
Updates to add a few words so that the post makes a little more sense.