Actually I do the opposite. I don't accept a claim until I've examined it against scripture. That might not mean I have to an in depth study of everything I hear someone say about God. As long as I can think of scripture that supports what they say and what they say isn't going against traditional long held accepted theology, I'm fine. If what they say sounds strange for some reason, I'll need a lot more proof from scripture before I accept it. Accepting every claim you hear and not dismissing it until you examine it can lead you to a lot of error since, especially in this age of instant and plentiful information, it's just not going to be humanly possible to examine every claim you hear about.
As for the claim of Russia invading Israel, if I remember right, I think Hal Lindsey based it on Dan 11:40 (ESV) "At the time of the end, the king of the south shall attack him, but the king of the north shall rush upon him like a whirlwind, with chariots and horsemen, and with many ships. And he shall come into countries and shall overflow and pass through." That was in the early 70's and he claimed it was going to happen within just a few years then the end would come. Someone supporting this, maybe Hal himself, even pointed out as evidence for the horsemen and chariots part that at the time Russia was the only country in the world that still had a standing cavalry, the Cussaks of Northern Russia I believe they were called.
Of course, his time frame came and went a long, long time ago and he was proven a false prophet.