The runways are not built to support that kind of weight for a plane like that. Miles City runways are stressed for 85,000. A landing 757-200 typically weighs just shy of 198,000. Now if they were enroute, say from New York to Seattle, and needed to divert, odds are they are well over that weight for fuel not burned.
The 757 absolutely CAN stop in the distance available, but the runway would be wrecked and they would have to disassemble and truck it out. Also, the simply fact is the pilots don't have charts, the airport isn't in the flight computer data base, outside of local knowledge they wouldn't know it existed. At altitude, enroute, faced with a major emergency, the pilots would choose a different option in all but the most catastrophic and extreme circumstances. Even then, it would take vectoring and visual conditions prevailing to attempt a landing. I don't know how low radar coverage is around there, but I would guess that Salt Lake Center (the controlling air traffic control facility) doesn't have radar coverage below 10,000. The scenario is just too far-fetched for a major airliner today.
As far as the Gazette article goes... A 757-200 typically holds 168-175, depending on configuration, a 757-300 holds 213. Who knows if they attempted Miles City. I am glad they didn't land.
The Miles City Airport won't go away. It isn't just going to close because Silver quits flying there. There will still be on demand charters and doctors and hunters and the usual business that comes and goes. I am sure BLM will continue to stage equipment there in the summer for fire fighting. I wish the community college would start a flight course, find the money to install a precision instrument approach and runway upgrades. It would be nice to get some of the oil money floating around and put it into the airport infrastructure before it is all gone again.