Re: But the good doctor hasn't been keeping his nose clean!
Under the current administration, just the DUI thing is potentially enough grounds to start deportation proceedings. As I understand it the rules for this date back to at least the Obama administration, but it's just not been stringently enforced until recently.
As to proof-of-insurance, in the U.S. this is now generally more automated and a bit more flexible than it may seem at first, although it can vary considerably from state to state. But if you note that at least six of the 18 interactions that I listed earlier concerned proof-of-insurance violations (the earliest in 1997, the latest in 2016), then you can reasonably assume that the good doctor is just generally scoffing at the law here.