Losing a tire at high speeds in any a/c could be bad, worse on a Sabre then other a/c because the gear is very close together. Only 7’2", as opposed to a citation XL at 14’ 9" The Sabreliner could be VERY screwy on the ground, I can only imagine that a blown tire could indeed cause the a/c to crash.
Back in my Navy days ( I can’t remember what stationm NKX or NQI) it was SOP to derig the arresting gear when a T-39 was scheduled to land. Apparently, the main gear could catch on the cable as the aircraft rolled across it…