Yeah, but a misdemeanor 5 years prior isn't exactly a major football issue.
It's not really "problem player" as determined by fans/media. I've read quotes from Belichick and Pioli in the past (when Pioli was with the Patriots) where they said that they talk to and/or evaluate the attitude of prospective players they're interested in and decide whether they have the right attitude to fit into their system and chemistry. If they decide the player does, that's all that matter...not past issues or reputation. And if they decide he doesn't, again that's all that matters. So what's important is whom Belichick, at this point, feels is a "problem."
This obviously doesn't provide any predictive power for fans, but that's where someone with good connections can provide some insight. Schefter obviously doesn't always get it right (as 44Thrilla noted) but he is a well-connected and well-regarded NFL reporter, so if he says that it's not going to happen...that doesn't mean it's in stone (since he can be wrong) but it does potentially provide a clue that Belichick doesn't view Jackson as a fit, attitude-wise. Whereas, Belichick obviously thought Moss was when he traded for him.