I said "lowers defence" to simplify things. No, it won't make your defence go down to 1 like it will level, but it raises defence very slowly compared to hit points, so if you want a balanced pet, you
will have to train both level and defence while getting strength and hit points from the lab. Otherwise you're going to end up with one of those very obviously labbed pets with crazy high HP, high strength and movement, defence several boosts lower than everything else, and a very low level. And it will cost a lot to balance that pet in the future... trust me.
Here's my pet when I stopped labbing. Note the high HP, fairly high strength and lower level and defence.
Here's when I stupidly decided that I didn't need defence and just trained level up, then strength.
Here's what he looks like now. You don't want to know how much it cost and how long it took to train that defence. Let me be a lesson! Train as you lab!
Edit: Oh, and on that "reset to level 1" thing, it doesn't happen once your pet is over a certain level. Some people say 10, some say 20. Some (and I am in this camp) believe you only get the "and he goes down to level 1!" message if, say, you're level 2 and the lab wants to take away two levels. Obviously you can't go down to level 0, so you get the "and he goes down to level 1" message instead of "and he loses two levels!" I
have heard of the level 1 reset happening to higher level pets, but very, VERY rarely, and I believe a staffer once confirmed that was a glitch. This is why all those big battlers lab without fear.