I’ve never read that and my take FWIW is “almost completely untrue”, *assuming *the fighters have already closed to weapons range.
The “maneuvering” a military jet transport, typical bomber, or airliner can do is minimal from a fighter’s or a missile’s perspective. A motivated transport pilot might force a miss on a strafing run or two, but won’t succeed the third time. As well, sound fighter tactics will ensure the fighter is never visible from the cockpit. Some military aircraft have scanners or gunners with some better view aft. But trying to have them verbally order timely maneuvers to the cockpit is unlikely to succeed more than once.
Something like a C-130 might have a better chance at success if it’s already at very low altitude. Much like fighting A-10s or helos, it goes so slowly that a fighter is either wallowing at his speed or flitting around at fighter-comfortable speeds like a bee buzzing a cow. The high relative speed makes it harder to get a cannon shot in the brief time between max and min range and increases the likelihood of the fighter goofing and hitting the ground.
What airliner-speed targets *do *have going for them is endurance at high subsonic speed. If somehow they know a fighter is headed for them and they turn tail and run, it may take longer for the fighter to close than they have fuel available. But that requires advance warning on the order of 100 miles and also the willingness to turn back. Depending on the heavy’s mission and other available defensive measures they may not be willing to run immediately.
AWACS is an example of somebody that will (they hope!) see fighters coming for them from a hundred-plus miles out. So they can turn and run at, say, Mach 0.8 while the fighter can only close at, say, Mach 1.5 for say 10 minutes before getting too low on fuel. 10 minutes at Mach 0.7 closure is about 70 miles. So if the AWACS (or whoever) finished turning around while the fighter is still 70+ miles away it’ll never catch up.
Obviously the range of whatever weapons the fighter has enters into it. In a co-airspeed tail chase most IR missiles are only good for another 5-ish miles. AMRAAM might be good for another 20-ish. The much longer ranges you often read about are based on the assumption the target and fighter are heading towards each other closing at 1000+ mph.
This conundrum was what lead to the 1950s development of SAMs and the received truism that “the bomber will always get through.” With the range of fighter interceptors and radars of the day it wasn’t practical to put enough fighters in the right spot in the sky to catch the bombers before it turned into a losing tail chase to the bomber’s drop point.
Very high speed bombers like Tu-160 or B-1A make the fighter’s problem much worse. More maneuverable bombers like Tu-160 or B-1B also make the problem worse.
At the same time, the advent of “supercruise” as the F-22 has and the F-35 supposedly has alters the balance the other way. If the fighter can sustain M1.2 or 1.4 for the best part of an hour, it can run down damn near anything from damn near any starting geometry.