So, you've expressed your opinion, but you have not defended it in the least. I posted an article that reviewed the literature (meaning...several studies were cited) that appeared in a peer-reviewed academic journal.
While you can continue to argue your point, it holds no substance.
A mile run may not be "distance" training by your definition, but it is continuous aerobic training as the article states. The aerobic energy system predominates the other energy systems (ATP-PC, Glycolytic) for any activity that exceeds roughly two minutes. It's been defined a little differently in different texts. I've seen some texts say 2:30.
When you recruit muscle fibers, you recruit the smallest fibers first and then move to the larger fibers. Your smallest fibers are your slow twitch fibers while the next size up is your Type IIa (Fast-Twitch Intermediate) fibers. The largest fibers are your Type IIb (Fast-Twitch). It is actually pretty rare to really be able to tap into those Type IIb fibers on a regular occasion. Usually, you're utilizing mostly slow twitch and Type IIb fibers. The type IIb fibers are the most influenced by training. Their enzymatic properties can shift towards aerobic mechanisms or anaerobic mechanisms depending upon the type of training that they are exposed to.
You're certainly entitled to your opinion, but research does not agree.
The best approach to training for gymnastics is interval training, power and speed endurance, and doing plyometrics.
The biggest challenge to a floor routine is being better prepared to deal with the build-up of lactic acid in the muscles. If you can increase your lactate threshold, that's the secret.