This one is for the @Innkeeper and I would be surprised if it was difficult to fix. 
Here is the issue, captured in screenshots from in-game on Elwynn server (with assisting annotation on images).
In these two cases, the (non-fatal) error is … a typo in the display.
My proof … can be found HERE at the 2007 web archive of the original Petopia site showing Pet Skills.
- Greater Stamina (Rank 1) requires Pet Level 10
- Natural Armor (Rank 1) requires Pet Level 10
As you can clearly see in the above screenshots, the Beast Training window is erroneously displaying Pet Level 1 … not 10 … as the requirement. This is a simple display error, because the game mechanics are working just fine (see: Target is too low level error message working correctly).
As far as errors go on a Vanilla server database, this one is definitely “trivial” … but it would be nice to see the fix for it get folded into vMANGOS generally (to benefit all vanilla servers), and our very own @Innkeeper is welcome to take the credit for it. 
Whenever time permits to roll out the update for this display typo error will be soon enough. 