Um...that seems a bit like a non-sequitur, but what the heck, it's a slow night at the studio so I'll play:
Educated or not, the "decision" whether some note "is" a 3rd can be made or not made; it's not mandatory to identify musical structures in order to enjoy them. However, sometimes identifying musical structures can enhance the enjoyment of music. It can be argued that the converse is also true. But, presuming that the "decision" whether some note "is" a 3rd is going to be made, it will be made for a reason: Either one of function (i.e., this note fulfills an expectation set up by the harmonic progression), or one of audiation (i.e., if it sounds like a 3rd it is a 3rd). No one should be calling something a 3rd if there's no reason to. Which doesn't mean some folks won't still try. It's entirely possible to have a musical situation where an E against a C#m chord would neither function nor sound like a 3rd...but A) that situation would be rare, and would almost certainly involve non-traditional instrumentation (otherwise it would be very difficult to not hear the E as the 3rd), and B) some folks, educated or not, would still insist it was a 3rd, simply because they bring the a priori knowledge that "E is the 3rd degree of the C# minor scale" to the table and don't recognize that sans functionality or audiation, that observation is purely trivia -- or baggage -- rather than actual information.
Was that the response you were looking for?