If the guy, in first place, started in first place and was in a faster car, you wouldn't be able to catch him. But you (the player) can not only catch him, you can do so within a lap or so, only after you've passed them for the lead there pace suddenly shoots up.
I've had this happen a fair bit through the course of finishing all the events in League mode.
Not only match, but surpass to set world beating times. I'm around about 2-3 seconds off the top10 times for any given track, sometimes around 4 seconds. Nothing crazy but not horrible either.
I can lap around a track, vs the AI in League mode, set a decent time on a lap where I have the lead for the whole race, and then the AI will smash it, not by a few tenths but by 3-4 seconds. I've had this happen in 1 make series too. The boost is comically over powered and even then, the AI is so inept they still pose little challenge.
Want a good example, Dragon Trail reverse. I did a few races there, last lap on the little straight before the (normally first) chicane the AI behind can make over a second just on the straight, regardless of car or exit of the corner leading to it. They have so much speed in fact that they can't brake in time and smash head first into the barriers. Though even after having to recover, still finish within a second or so at the line