When I got a tiger companion in the game I play in, my DM and I went back and forth over this wording. It's sucky and illogical, IMHO.
We settled on something that generally makes pounce less valuable, but more rational: pounce can be used on any opponent who is denied a dexterity bonus.
If a tiger wants to pounce in the first round of combat, he'd better win initiative: if his opponent gets to ready her sword, the tiger is gonna have trouble pouncing successfully.
However, if me and my buddies are attacking a party of orcs, my tiger can sneak around onto a ledge behind them and then pounce. Alternatively, our friendly local wizard can cast invisibility on the tiger; once he's done weirding out over his new appearance, he becomes a nasty pouncer extraordinaire.
This is, obv, a house rule; it's more consistent than the real rule, I think.
Daniel