That simply isn't true.
The D-9 can't quite run an La-7 down, and even if it could it'd be dogmeat because the La-7 literally does everything better. The La-7 turns better, accelerates faster, climbs better, handles better, and has more firepower. A D-9 that "runs down" an La-7 better be ready for the fight of its life, because an average La-7 pilot with basic knowledge of the two planes will hand a "expert" D-9 pilot his ass. For what it is worth, the D-9 rolls better, although I fail to see that as a significant advantage.
The 109G-10 is like an La-7 "lite". It accelerates almost as well, climbs about as well, turns almost as well, rolls almost as well, handles almost as well. It is significantly slower, which means it has almost no chance to run an La-7 down, and it doesn't have the firepower to spray at a fleeing La-7, although it will hang back in theoretical "firing range" for a while. A "turn-fight" between an La-7 and a 109-G10 is just about even, although the La-7 can leave whenever it wants to and the G-10 will never catch up again.
The Typhoon is like a Dora, except it accelerates better, climbs worse, turns better, and rolls worse. This means that the La-7 is faster, turns better, accelerates better, climbs better, and rolls faster than the Typhoon. Although the Tiffie packs some serious firepower, it had better land that shot to kill the La-7 it is chasing if that La-7 decides he is going to force the issue, because once the fight starts it is decided advantage, la-7. Plus, again, the La-7 can leave a fight once it starts at any time it wants to, because it has a decided acceleration advantage and a marginal top speed advantage. A fleeing La-7 is in a lot more danger from a Tiffie spraying 600-800 yards off its 6 than it is from a G-10, but the Tiffie will never close the distance again.
The P-51 is actually the fast plane that is least like the La-7, in my opinion. The 190D-9, 109G-10, and Typhoon can all be looked at as "failed La-7s", in that the La-7 does everything they do, except better (with the exception of packing Hizookas). The P-51D is a little different, in that it has a decided advantage over the previous 3 (and the La-7) in the low speed "fighting" department. Around 180-200 mph, a La-7, 109/190, or Typhoon with a P-51D on its bellybutton is in serious trouble. Unless they can force the P-51 to miss that one shot it just bled all that energy off for. Then the P-51 is in serious trouble, because the Pony's one serious flaw is it accelerates like crap compared to the rest of the late-war speed demons. So once you get a P-51 down to 150 mph, and you are in a 109/190/la7/typhoon, you can accelerate for about 30 seconds and build up an energy advantage, then switch over from angles tactics to energy tactics. The P-51 is screwed in that case, because it won't be able to generate enough energy to get back on an even footing with you.
As the La-7 is the best turning "fast plane", the P-51 doesn't have much of a margin of an advantage over it in the manueverability department. From about 150-200 mph the P-51 will turn better because of its flaps, but if that happens the La-7 can relax its turning to build up some energy, then get above the P-51 and kill it with impunity. A P-51 that decides to chase down an La-7 better either be very cautious (in which case the La-7 waits till the P-51 zoooooooms, then takes off running again, building up a larger and larger seperation between "passes"), or very aggressive. If he is very aggressive, he better hit that shot, or the La-7 will turn the tables on him, or (more likely in the MA) realize he has gotten the P-51 slow so he can take off running again and not get caught this time.
That'd be my analysis of the relative strengths anyway. Nothing new there, btw.