The exfiltrated exFAT driver

Absolutey, GPLv3 probably has little influence on GPLv2. But both are based on the same legal system, and so if downloading a new copy granted you a new license in GPLv2, it should do in GPLv3 as well. GPLv3 behaves as if that's not the case, so GPLv2 is (probably) equivalent in that respect.

But, like I said, I don't believe that anyone's attempted to test this specific case. To the best of my knowledge, no GPL cases that have gone to court have attempted to claim that they'd gained a new license through an additional download.