You sometimes have end around taxiways that are at one end of the runway and can be used when active. But that could be a massive diversion.

I know that Heathrow have multiple fire stations and rendezvous points for emergency services so that fire service can attend even when one runaway is closed to crossing. This could be needed to allow continued operations following a crash. It allows them to accept emergency landings more easily whilst maintaining emergency service to another active runway.

The fire station was located on the opposite side of runway 4 from the United plane. To avoid crossing the runway would mean having to travel a few extra miles around the thresholds (I assume).

I guess they could have found a route that wouldn't conflict with landing aircraft, but I doubt that's a practical option most of the time.

Plotting a course on Google Maps, I think this would add ~1.4 mi if you go around to get to the other side from where they were.