If the sender requests GPLv2, he should receive GPL version 2.

If the sender requests GPL, I find it natural for him to receive version 3, because it's the latest version. At the time of receiving the license, he gains knowledge about the existence of version 3 (the header on the print says the GPL he received is version 3).

If the sender has a notice about GPLv2, it means that there's a high chance that there's also GPLv1. This should be a sufficient hint that requesting only "GPL" is not sufficient, because the sender should be aware of the risk of receiving GPLv1 if he won't mention the "v2".

GPLv2 by default means GPLv2 or later, so GPLv3 is perfectly valid indeed.