I'm not saying intentionally drive around uninsured, but I'm sure this sort of thing must arise from time to time, confusion/mistakes changing over insurance etc after newly purchasing a car.
Confusion does indeed happen, my ex did a transfer of insurance online, and for some reason it didnt go through properly even though it looked to her like it had done, she then got stopped driving her new car, which she believed she had transferred insurance to, and she got 6 points on her license.
She was a legal adviser for the citizens advice bureau too so not exactly some boy racer they had it in for, but neither the police or the courts had any interest in that she genuinely believed it had swapped over earlier that day when she did the form online, they just stuck to the basic fact that the insurer said she wasnt insured. Confused or mistaken or not, if you arent insured and they find you driving, you are going to get 6 points for it.
I'd just stick to my second point, check the car is still insured.
Even if it is still listed on MID, and hence the police are unlikely to give you a problem, if you actually have an accident and it gets looked into your insurer may well claim that actually its not insured by the previous owner anymore as the terms it was insured under by them is that they are the owner/registered keeper, and seeing as they have now sold it, their insurance is no longer valid even if it is still running.
Personally if I was the OP, id make sure whatever I did was above board as the points and the fine arent the issue, its trying to insure your car again afterwards, insurance companies put huge increases on for IN10/IN12 etc, as far as they are concerned doing an insurance company out of money is a worse crime than mass murder.