It's easy to reassign a value like that to whatever you want.
1) Go to Tools/Options and click on Keyboard (under environment). Then find the command associated with F12. Which one depends on which mapping scheme you use, so I can't tell you the one to find.)
Then change it to whatever you want.
Too bad I can't add comments...
When I type in F12 (for Press shortcut keys), I get Edit.GoToDefinition. If I remove that assignment and then try again, it shows how it is used with Page Inspector.
If you enter F12 and nothing shows, then you can assume that VS is not using F12 and something else is.
You can just try assigning F12 to something and see if that is called instead - then at least you will have some idea of if VS is controlling it or something external to VS is.
Remember that you could also have some application that has remapped F12 so that when you press it, your application is getting a signal that some other key or key combination has been pressed (happened to me once.)