Do you want to be right? Or do you want to live a productive life?
Validating every proof that comes across your table would quickly chain you down, verifying everything. Clearly there are points where we have to make judgement calls as to what to do with the proofs we don't have time to research.
Do all arguments have to be accepted hook like and sinker? Perhaps there is something between "total hearsay" and "formally proven" which has some elements of both. If you can find one that works for you, you can attribute some level of confidence in an argument and work with it. Baysean inference is one which I have found useful, but I recommend you find what works best for you.
If you're in the middle of an argument, and your opponent needs you to fully accept their claim on faith in order to continue, then the onus is on them to convince you that the argument can continue.
The other approach, which I find highly productive, is to try to steer the argument in such a way that the veracity of the final result is no longer dependent on the claim being made. If I claim "blue is red," a highly tricky claim to make, but our eventual goal is to figure out what game to play tonight, you may be able to work around it so that we both agree that, regardless of whether blue is red, the game we'll choose is the same.
If they wont take the time to work with you so you can understand the research behind their claim, and you can't nullify its importance towards the final result, then you're in a region of argument that is quite complex. There's myriad ways to go forward, at least one for every pair of people on the planet who disagree about something (which is quite a few!). However, I have found that, if you break up the problem enough, it often will fall into one of those two categories, and the problem can be solved accordingly.