Try it by all means, but it's virtually certain that the problem is with Windows 8. A Scheduled Task should not invoke a UAC prompt (for precisely the reason you pointed out / complained about), whether the process it is invoking (i.e, SE) is asking for elevated privileges or not.
Re-installing SE won't change the fact that by its nature SE will ask for elevated privileges (because it needs them to deliver advertised functions). The point being that Windows should grant them if an Admin set up a Scheduled Task that asks for them (without UAC prompting).
As this only started when you changed Windows version (but you are not the only Windows 8 user out there, and none of the other W8 users seems to have an issue with Scheduled Tasks versus UAC), you can maybe draw the same conclusion - a Windows glitch of some kind...
Re-installing SE won't change the fact that by its nature SE will ask for elevated privileges (because it needs them to deliver advertised functions). The point being that Windows should grant them if an Admin set up a Scheduled Task that asks for them (without UAC prompting).
As this only started when you changed Windows version (but you are not the only Windows 8 user out there, and none of the other W8 users seems to have an issue with Scheduled Tasks versus UAC), you can maybe draw the same conclusion - a Windows glitch of some kind...