Nah, that's untrue. I usually end up with anywhere from 5 to 10 Chef's Knife items after I've acquired Tonberry.

Like Skyblade said, most guides will state that you need to kill 18-22 Tonberries, before the king appears. It's very easy to lose count; he usually shows up for me at around 21. During my current playthrough, he showed up at 19 (I think).

The easiest way to kill Tonberries is to leave Squall's HP in the yellow and be liberal with his Renzokuken limit break. The only attack they use before they get close enough to knife you is Everyone's Grudge, and that will likely KO a Squall with 9,999 HP anyway, depending on how far you are into the game, and how frequently you fight (the damage dealt by Everyone's Grudge is based on the number of enemies the character has killed - and Squall has probably killed about 80% of your enemies).

A Spd-J junctioned or Auto-Hasted Squall with a high Str stat should be able to take out Tonberries with one or two Renzokuken's without getting interrupted. If he does get KO'ed by Everyone's Grudge, a Phoenix Down is all it takes to raise him and put him back into limit break-ready form.