The site owner's response is correct to some extend, because dice process data seems not on chain, e.g. chance to win, bet size etc.
But if the dice info is part of transaction which will be on DAC/BTC chain, you can play without necessary to deposit, you are the owner of the privkey.
For comparison, you can have a look of classic satoshi dice, but any way, there are other potential issues with their random seed.