Whose insurance is responsible for injuries sustained in single vehicle accident - driver's or owner / passenger's?

It's most likely that the owner's insurance will have to cover this, as it's usually considered the "primary" coverage.  However, depending on how the two insurance policies are written, it's possible that the two insurance companies will have to split the cost, based on their "other insurance" clauses.

Most insurance policies include language about what happens when there's coverage for an occurrence, but there's also another policy that covers the same loss.  The simplest form of this is little more than, "If there's other insurance, they pay," although modern forms usually have at least some language about how the cost is to be split up.  Then, the "other insurance" clauses of both (or all, if more than 2) policies have to be reconciled, and that's a very, very technical point of insurance law.