Speaking as an FC during the Lightning era, high level intercepts were frequently scripted to ensure AAR support. I frequently intercepted U2, SR71 and Mirage IV during exercises, but alweays with a bit of pre-notice.
To give an example, during the 70s and for WT Tacevals, the French woud send Mirage IV up the North Sea to fly back down top France at FL650+ and M2.0.
LATCC would give a heads-up as they headed north and an F3 would be scrambled to plug into a tanker at the tropopause on track (the FIR boundary) and wait, staying plugged in. When the Mirage broke cover the F3 would be pulled off the tanker at about 150nm and do the intercept with full tanks.
On one occasion the F3 only had Firestreak and was rolled out on a U16A (180x26 converting to a 90 crossing leg) at 6nm. He (the Wandering Milliamp) closed to 1nm, called Fox 2, and then diverted into CS because he couldn't make WT 30nm south!!
I was at Boulmer during the last few months of the Lightning when several pilots tried to see how high they could get. They'd tank on TTL 8 or 4 and be dropped off about abeam Newcastle and then parallel the coast heading home, aiming for the top of the dive arc, 35nm off the coast.
At least one ended up flamed-out tumbling end over end ballistic until he recovered control and relit as he passed overhead the Aggressor Area. Heights as tracked by height finder (HF200) wase in excess of FL850.
The official ceiling was FL560 because they only had standard flight suits/oxygen etc. So if the canopy had gone, they'd have had no chance. But since when did fighter pilots care about that?
Not here-say. Been there, done it, got the T-shirt, as they say.