Well, to counter the argument Ash and Trip both got Snivy. That in theory, might be true. But... when Ash owned Snivy, Trip had Servine. Bianca had Tepig, but it was evolved into Pignite when Ash had Tepig and again it evolved into Emboar when Ash had Pignite.
Same with Paul... Both he and Ash owned Torterra. Again true... but when Ash had his Torterra, we didn't saw Pauls anymore (Despite being his starter and main Pokemon). Alexa didn't appear anymore in XY when Noibat came into play.
Thus all the arguments you make are kinda pointless imo, since you can say: Misty owns Politoed, this didn't stop Tierno to get own. Ash owns Charizard and Unfezant, didn't stop Trevor and Alain. Sawyer got Sceptile, despite Ash having one.
Thus the conclusion is: If a Pokemon is owned by a MAIN character, the rival who owns the Pokemon (Paul), will not showcase said Pokemon anymore. Tierno could have Politoed, because Misty didn't appear. Same goes for Alain, Sawyer and Trevor. They could have said mons, cuz Ash weren't supposed to show up and thus they could showcase the Pokemon... while Ash only showcased the Kalos mons. Same case with Noivern. When they decided Alexa wasn't needed (Or her Pokemon weren't needed to appear on-screen), they gave Ash a Noivern to showcase the line, since Clemont already owned Heliolisk. Thus... we can say with a certainty Ash will not own a Pokemon a Travelling Companion has. But... that doesn't mean we can already rule out Popplio (Example), since at this point we don't know if Lana is a travelling companion or just a recurring.