This is 100% true. If you're at level 100, you can train your strength or defense (or movement) up to 200 and your hit points up to 300. However, once you go over 2x with hit points, you can only train hit points further (up to the 3x level maximum). No more strength or defense while you're doing this.
I did do this, thinking I wanted it, but I was wrong. In my humble opinion, you should increase HP to 3x at the end of your training journey not the middle!
I kept strength, defense, and hit points 2x my level up until about level 280 when I noticed for the first time that one could up the hit points to 3x the level, so I went wild and got my hit points to 840 before I realized I could not train my strength or defense until I reached level 420. All I could do for 100+ days was to train level and nothing else.
I have done the math (after doing all this, not before like a sensible person) and depending on where you stop training strength and defense (there's no reason to go higher than 750), it's between 11 and 14% cheaper red codestone-wise to train everything up 2x until you hit level 500 and then increase hp as much as you want.
Realize that no matter what, you're in for finding 1200 to 1500 red codestones. Not having to buy 200+ extra codestone is obviously cheaper and will take several weeks less to complete, but that's not why I'm warning against going 3x early. I can tell you the sad grindy-ness of level day after day made me hate the game:
If I got to do a faerie quest that gave me 3 HP, I got mad! You should be happy something that would cost 300K np to do cost nearly nothing, but my joy had been ground down to a nub.
In those days and days of grinding level out, I passed the Adept and Advanced levels of training, so once I reached the 2x limit, all my progress on strength and defense cost 3 red codestones. I had to skip over the 2 codestone cost entirely. I felt that I'd missed out on the cheaper tier even though mathematically it was only for 14%, it still made me grumble.
Maybe if I'd chosen the path purposefully at the start, I wouldn't have felt that way, but all of a sudden realizing I had to level up about 200 times before I could change anything else wore on me. And, of course, some players are going to be fine with it, but I think you're better off knowing what you're up against beforehand.
(I'm better now that my pet's levels and stuff are properly aligned)