No, you're not interpreting that correctly. If someone is drinking anywhere on the premises that is covered by the license, you're not allowed to be carrying. You're not "good to go" just because you've got a room or patio to yourself, for example. In theory if NO ONEin the entirelicensed establishment isdrinking alcoholyou would be within the law. But it's pretty hard to ascertain that without difficulty.
By contrast, if an establishment has a Class D liquor license that doesn't cover Sundays, and the place is open on Sundays, to the very best of my knowledge (and in agreement with what I've read on the OFCC forum), it would be okay to carry under those circumstances.