I admit it, I studied journalism a very long time ago when they still drilled us on our role as arbiters of truth and other quaint notions. At the risk of making a suggestion that might cause the White House press corps to go old school for a day, I think it would help establish your zero-tolerance for being stonewalled if you were to, well, not put up with being stonewalled.
My simple suggestion: The first time Press Secretary Sean Spicer ducks a question at the next White House press briefing, the next reporter called upon asks the same question and demands an answer. When Spicer gets irritated and again refuses to answer, the next person called upon follows up with the same question. And so forth. If you use up the entire briefing with that one question, so be it — it’s not like you’re getting information and news anyway.
This will draw a massive line in the sand, probably blow up like crazy on social media and make your point in an undeniable way.
You can do something like that or you can make the news that the people covering the White House got played for chumps yet again.
It’s your choice how long you keep letting this happen.