For instance, I was chased by a fer-de-lance with a lower base speed than mine, so it was losing ground both at normal speed and at full injector speed (X7). However, when I switched to X4 injector speed, it was also losing ground at more or less the same rate.
PS:
Well there's one case when the AI uses its injectors to catch up: when you're not looking

Switching back and forth views, I can see them losing ground when I'm looking at them, and catching up on the scanner as soon as I don't.
I think this behaviour could advantageously be replaced by something like (if it doesn't exist already): use injectors when about to lose the target, until the ship is in weapon range.