Your insurer, not you, makes the determination of whether they have to or should (e.g. to avoid expensive litigation) pay a claimant, so ultimately, this is up to your insurer. Even if she was not supposed to be there, if you were negligent or careless in some way and caused the accident, you are still liable for her damage or injuries--it may be that she can and will be ticketed for her violation, but there is no legal exemption from liabilty because the person was doing something illegal. That's why jaywalkers who are the victims of hit and run can sue or will get a payment from insurance; that's why, in a famous case, a trespasser whose leg was blown off by a bobbytrap (a gun on a tripwire) a homeowner left at his house was able to sue for a great deal of money. So the issue is whether you were at fault in some way--that, not whether she could be in the HOV lane, determines whether she may be entitled to compensation.If the tire blew out, you are probably not a fault unless it blew out because you were driving excessively fast or carelessly and hit a curb or debris and caused the blowout, or had drastically overfilled the tire.