You do not know who has an emergency, and who doesn't. You don't get to enforce one law (speed limits) and flout the other (yield the passing lane). In fact, you don't get to enforce any laws if that isn't your job, and if it were your job, you should not disregard one of those laws.
Edit: According to this resource[0] only 4 states require you to yield to faster traffic approaching from behind in the left lane, so this seems to be far from a universal requirement.
1) Yield the passing lane for anyone that wants to go faster
or
2) Yield the passing lane if lane on the right is free.
I am asking because I am not sure, but (2) would make more sense to me. You should not be required to break the speed limit to be allowed to pass the slower traffic.
It's very, very simple.
BTW, in Texas it is now legal to pass on the right because of all those who fail to yield the passing lane. Passing on the right isn't very good, but it's what you get when people decide that the left lane is for themselves.
To your other point, it is not "flouting the other" law (yield the passing lane) if its 1 person doing 100 mph trying to pass you. The law is in respect to the "normal" flow of traffic, not the fact that any one person is trying to go faster than you.
During this drive, the speed limit mattered very little to me, and I drove as fast as I possibly could.
Whether this was "right" or "wrong" isn't something that crossed my mind at the time. When one's own life (or the life of a loved one) is on the line, people have a tendency to do things that don't make sense to an outside observer.
Luckily for us, we arrived at the hospital without further incident, and my father was quickly cared for. I didn't time the trip, but I imagine it was only marginally faster than driving at the speed limit, as my vehicle at the time wasn't particularly fast.
It doesn't mean there is a law granting us permission to do so, which was the part of the comment I replied to that I took issue with.
Its just something that is gray and we have to do when we need to.
It is the same logic as the, "I'd rather be judged by twelve than carried by 6" crowd, interestingly.
Not directed at OP, but I wish more people understood this!