It absolutely should not do this, as it should not do what it does now. It should be configurable at the application level by the administrator.
For some communities, how it works now is perfect. For certain communities depending on how they use applications (as is the case with Downloads on this community, but not all), the administrator here should set the default for the Downloads app to be app first, unless end user picks "everywhere" from the scope selector.
Adding granularity at the application level to set a default search context increases flexibility and user understanding.
I say all this knowing that for our community, I'd keep it on a global search. But I possess the critical thinking skills necessary to know that one shoe does not fit all.