And the Invisibility Cloak may have been exceptional, but it wasn’t infallible. A gifted wizard such as Dumbledore could, for example, disturb the dust in a manner which revealed the absence of air in that part off the room. Also, Dumbledore probably heard voices before he entered, and he noticed that the room had only recently been vacated, and he could easily guess who. From there it was easy to notice footprints, breathing or the like that gave away their presence.
Add to that that he had been with the Minister up until then, and could hardly excuse himself to eavesdrop on Hagrid’s conversation. And knowing they were in the room wouldn’t tell him where in the hut they were hiding anyway. This part of the theory certainly doesn’t stand up to even mild scrutiny.
Duke