You're right that they are not obliged to say how many. But on what grounds do you take that as allowing the other side to not match numbers? You can't make up laws to suit yourself. As long and the non throwing-in side has time to reduce numbers you should manage things. Which may mean a warning of ping first time but you can't assume it's full.
If they don't communicate to me, then I'm sole judge of fact. The fact is they might've made an error in their counting. They may have miscommunicated the numbers to their team mates and they might want a full LO but 2 of the forwards haven't heard. So I tell them at the start, if you don't tell me your LO numbers I'll assume it's a full LO. There's nothing in the Laws that prevents my standpoint. If they tell me then yes, I'll ping the non-throwing team if they've had plenty of time to drop numbers. Although, I'm there to facilitate a game of Rugby, not ping every minute offence and turn it into a game of kicking penalties/free kicks for gains in ground etc. So if the throwing team don't tell me, how an I meant to know their intensions. If you establish the ground rules at the start of the game, it's easier to manage and let the game flow.