Think about it this way: the license is "GPLv2 or later", not "GPLv2" or "GPLv3". If you change the license notice, you are changing the terms in which people will receive the code from you. The GPL (both of them) clearly says you cannot do this. You have to distribute modified works under the exact same terms you received the original work, or you lose the right to use the software (both original and modified) yourself if you violate its licensing terms.
IANAL. I'm more familiar with GPLv3-or-later because it's how I license Red Moon, but I assume v2-or-later uses the same phrasing, which I got from the FSF website iirc:
> Red Moon is licensed under the GNU General Public License version 3 or (at your option) any later version by the contributors.
As this reads to me, I am offering you a choice of licenses. You may use Red Moon under the GPLv3, or you may choose a later version of the GPL. Or, you could choose both, if you wish to distribute your derivative as GPLv3-or-later.
Put differently, a GPLv2-or-later currently means a dual-license, under both v2 and v3 (and an automatic relicensing to triple license if v4 is released, etc).
The standard wording for a GPLv2-or-later license (as recommended by the appendix of GPLv2 itself) is:
> This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
Per that notice, I have an option of distributing it under the terms of GPLv2, or under the terms of the GPLv3, or even a GPLv4 if the FSF were to someday publish one. So, I decide to make use of that option and distribute it under the terms of the GPLv3.
You can't argue that from the text of the GPLv2 or GPLv3 that I don't have the option which the license statement says that I do. The license statement applying the GPLv2 (or GPLv3) text is of greater authority than the text of the GPL itself. You can't use the later to cancel out the option granted by the former.
The license is allowing you to perform specific actions. You can modify the work or redistribute it under the terms of "GPLv2 or later" without losing any of the rights the original copyright holder(s) passed on to you.
For a "modify and/or redistribute" example, under this "GPLv2 or later" licensing you can modify the software and use it in a SaaS without having to distribute it (which the GPLv3 would force you to), because you can choose to follow the terms of the GPLv2.
Likewise, you can use it and demand/assume implicit patent grants from the copyright holder, which the GPLv2 says nothing about, but the GPLv3 does.
Changing the license of the work is not modifying the work. That is the key difference. You must pass the same set of rights which you have received, like I said in other places. You can modify the work, but you cannot relicense the work. Only an original copyright holder can do this (for its part of the code).
When someone licenses software under the GPL (any of the versions), he/she isn't giving recipients any rights over licensing, he/she is only defining how the software can be modified and distributed.
Edit: To be clearer, a specific GPL version says you must pass that specific version's rights when you distribute. This makes it look like when you choose a version, you only need to pass that version's terms along. However, general copyright law (in most places) says you need to be explicit, so, if the GPLvX doesn't say you only need to pass those rights, then you need to pass those rights and any other (perhaps optional) rights.
> For a "modify and/or redistribute" example, under this "GPLv2 or later" licensing you can modify the software and use it in a SaaS without having to distribute it (which the GPLv3 would force you to), because you can choose to follow the terms of the GPLv2.
GPLv3 says absolutely nothing about SaaS. You're thinking of the AGPLv3. The only thing GPLv3 does in that regard is declare itself compatible with the AGPLv3, so you can combine code under those licenses.
The answer is "Yes".
Think about it this way: the license is "GPLv2 or later", not "GPLv2" or "GPLv3". If you change the license notice, you are changing the terms in which people will receive the code from you. The GPL (both of them) clearly says you cannot do this. You have to distribute modified works under the exact same terms you received the original work, or you lose the right to use the software (both original and modified) yourself if you violate its licensing terms.