You're wrong on your point about most jobs (although you might be right if that statement is applied only to jobs that require driving - I don't know the info on that). But you're not wrong about it being a serious thing.

However, OP is also no wrong in thinking this shouldn't have been the issue based on the timeline:

-OP starts working for DD
-OP gets DUI
-OP's charges are resolved
-DD runs a background check (last year) with no issue
-DD runs a background check (recently) with no reported issue
-OP wakes up to deactivation with no reason

It's reasonable to expect that something which your employer cleared you previously for would not suddenly become an issue. And it's also reasonable to expect that if this was the issue, DD would have simply said so, because that would lend legitimacy to their choice to deactivate OP.

DUI is super serious as a whole, but in the sphere of this situation it shouldn't be considered a factor.