I gotta say I dont feel that im making a "just play around it " argument. What I'm saying is that it is possible to do so with some deck types.
The reason this is different than higher caliber is because higher caliber put you in a situation where if you didnt use responses as answers to cards you were going to lose to the deck anyways, Owlface does not. Decks like hanzo loop of FTK felecia can easily circumvent the card, and a lot of decks run things that are generically an answer such as I-Spin.
Also I should say this once again supports my stance on making more high check attack cards and such. A lot of people use as many foundations as they do because they literally have to just for the checks and to pass checks later on. Thusly you are forced to use more foundations that are subpar to your core foundation base and gives your opponent a lot of oppurtunities to give you sub optimal foundations. If people could build decks with higher check attacks, actions, and foundations they could run less foundations overall, using a higher percentage of the always desirable foudnations and giving Owlface less to pick from. Lynettes and Valerias shops for instance are actually great tools for fighting owlface. They are immune to him when in the discard, function to accelerate your game when in play, amazing blocks and 6 checks. Run them and include only foundations like illegal maneuvers and Blood runs true and your opponent will be hard up to owlface your staging area at all cause they may wind up not having anything to give you. Sadly illegal maneuvers just makes owlface better again but it pretty much makes any asset better.
Ironically one of the reasons i like preparedness and Kims Dojang are because they are assets that can help you pass your checks and thusly give your opponent less options to either deal with them or give you worse foundations for the ones in play. Too bad they are character specifc and unique.