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If you install NB 7.1.2 bundled with JDK 7u4, both JDK 7u4 and NB 7.1.2 are installed on your system as separate programs in the Windows Control Panel:Programs list. You are able to the UNINSTALL JDK 7u4. However, if you do so, it is impossible to uninstall NB. If you try, you get the same error dialog. Apparently it does the JDK-requirement-check even when you are trying to REMOVE NB. If JDK can be uninstalled independently, NB should too. It is silly to make the user re-install JDK just so they are allowed to uninstall NB.
One possibility is to move temp JRE to NB installation folder after installation and uninstaller should use this JRE to run on. Of course this JRE should be deleted after uninstall by native uninstaller part.
No plan to solve this, seems to be too expensive to bundled JRE with about 20 MB for this (corner) case.