Correct, but part of those stats that ilvl increases is the level of the pet, up to 119. I think that part was adjusted in a later update, tbh I can't remember. They staggered so many updates, pet levels/stats, Blu stuff, etc. Pup was ahead of the curve in all this cause it got it's Animator from Delve, where as Bst, Smn, and Drg didn't get their fixes for a few more months.
I don't know the details (not a Bst), but I'm sure Dasva or Falkirk could better explain the level properties of Bst pets. Some have their cap set low enough that Beast Affinity merits will get them to the 119 cap, while other's have their cap set high enough that the merits do nothing.
Regardless, ilvl gear has absolutely nothing to do with it. It relies solely on the ilvl of the main hand weapon.