Or, that result is just an artifact of how most driving happens within a few miles of the driver's home.

If 70% of one's driving is within 5 miles of one's home, but 55% of accidents occur in that radius, then people are indeed safer drivers near their homes -- probably because of familiarity.

"Most accidents are close to home" is a Stat 101 Day 1 example of fallacious statistical reasoning.

Hint: what do nearly all routes driven have in common?

I do know that if I never go within 20 miles of my house, I have an 80% chance of living forever.

Source? It seems much more likely that most accidents happen within some smallish radius from home because one is much much more likely to be driving there as home is the presumably, on aggregate, most frequent starting or ending point for a person (besides, possibly work or a transit hub, etc.) – the other end points are much more dispersed, but home definitely biases the distribution of driving location and therefore one would expect to see more accidents near home even if the moment by moment probability of getting into an accident was uniform.

Two people have made contradicting claims, neither with a source.

Unless there is evidence stating otherwise, I am going to go with the null hypothesis that people drive the same no matter where they are.

Certainly knowing an area can breed inattention, or risky behavior based on familiarity. My hunch is that it still works out to be safer on average, but admittedly I have no data for that.

I was always under the impression that accidents happen close to home because that's where people spend most of their time so they get a lot more chances to have an accident there.

Most accidents happen near home because most driving happens near home.