Will reporting accident while someone else was driving cause our rates to go up?

[Jonathan Kamens]

We left our minivan parked in the driveway of a relative's
house in NJ while we were spending the weekend in NYC a few
weeks ago.

At some point he decided he needed to move the minivan into
his garage, apparently because he was worried about it being
broken into (he lives in a beautiful suburban neighborhood,
so I find this somewhat puzzling, but he claims that people
troll his neighborhood looking for cars to break into).

In the process of doing so, he managed to bang up one of the
rear panels of the minivan pretty badly. When we came to pick
up the van, he said we should just get it fixed and he'd pay
for it.

We took it to Stadium Auto Body in Brighton this morning to
get an idea of how much it cost, and they said it would be
well over $1,000 and we'd have to get a rental during the
repair, which add to the cost, because it would take 1-2 weeks
to fix.

Given that our auto insurance deductible is $1,000 and
includes rental coverage, it starts to look more attractive to
report the accident to the insurance company and get it fixed
through them, and have our relative reimburse us for the
deductible, rather than for the entire cost of the repair and
rental.

The question, however, is this: will our insurance rates go
up if we report an accident that happened when someone else
was driving the car?

I understand that the insurance companies (ours is Liberty
Mutual) have some programs for reduced rates for people who
go for some number of years without any accidents, but I'm
not talking about those, since I don't think we have any such
discounts on our policy. I'm talking about the whole SDIP
surcharge thing that happens in Massachusetts.

My assumption is that our rates won't go up since neither of
us was driving when the accident occurred, but I'm curious if
there's anyone here who can confirm or refute that with
certainty.

Obviously, I'm a bit reluctant to call the insurance company
and say, "Just theoretically speaking, suppose someone else
damaged our car while driving it and we file a claim to get
the damage repaired. Just theoretically speaking, again, will
our rates go up?" That would seem a little hinky to them, I'm
sure.

Thanks in advance for any advice you can offer.