If they had left in the 'or later' clause they could still use it under GPLv2, just not _limit_ it to GPLv2, which is what the 'third-party software vendor' decided to do.
If they had left in the 'or later' clause, they couldn't use software from the third-party supplier, who only licensed under GPLv2 without the 'or later' clause.
If you are distributing someone else's software (even as part of your own work), you are restricted by the terms of the license they've given you. If that's GPLv2-only, you can't distribute a work incorporating their work as GPLv2-or-later.
If you are distributing someone else's software (even as part of your own work), you are restricted by the terms of the license they've given you. If that's GPLv2-only, you can't distribute a work incorporating their work as GPLv2-or-later.