VNs here give a realistic portrayal about how Hollywood portrays women. No matter whether they're 16 or 42, the actress will always be in her mid twenties ...
The liking of this particular device aside, there are things that can explain this:
(a) the MC of course should know all details of the accident
(b) he however never needs to have met the mother, everything could have been done by lawyers (unlikely but possible)
(c) she is not forced to follow civil proceedings against him. For one, it might not have been looking like there's much to get at that point in time (he became successful later, but then of course there's the probability that his family had money given the car the MC drives), more importantly many people want to close this chapter of their life as soon as possible
(d) in some jurisdictions, criminal charges are dropped or punishments severely lessened, if the "self-punishment" inflicted by the crime was large enough. So a 3 year sentence (just an example) for drunk driving with fatal outcome may be outshone by the time the MC spent in a coma
So if this is more or less what happened, and then the mother still couldn't find peace and decided to approach him without giving a warning, this could work.
It is indeed a bit strange right now but maybe the continuation will give us more information.
Of course, legal plot holes (and plot holes of what happens afterwards) are a staple of media, albeit an unwelcome one. Don't get me started on my pet peeve: contracts signed under force/blackmail are somehow deemed legally binding despite all that is known to the public.