If you decide what's behind the door before the PCs get there, they have real options of what door to open with real consequences. If you decide whats behind the door when they open it, then it was just a phantom choice, and that's the problem with sandbox play as I see it. Lots of flag waving about player freedom and choices and in the end still its just a DM making up whatever he wants after each player "choice", thereby making those "choices" trivial or meaningless.
That's not what most people would consider a sandbox. What you're describing is at least partially encompassed by the term "illusionism" and is typically used when a DM has prepared material they want to use, or to keep a plot-based adventure moving in the right direction.
It seems to me that a number of people who preach a sandbox approach one of the most important aspects is that the DM has as little input once the game is underway, where everything is placed before the players make their decisions. Either the stuff is where the DM placed it, or it's determined randomly, but the DM isn't supposed to "impose their will" on the game otherwise.
In a sandbox, exploration is paramount. If they characters are looking for a lost tomb, the location of the tomb is already known to the DM. It's a question of whether the characters can find it.
Nowadays, I see a lot of recommendations against this, for several reasons. First, the DM puts in a lot of pre-session preparation, for lots of material that will never come into play. In addition, if there is something specific the characters are looking for, it can sometimes take several sessions of exploring to find it. So techniques, like the one you don't like, are recommended or used. In some cases they are tied to player choice/character skills.
For example, instead of having to actually stumble across the location of the tomb by picking directions, following clues, etc., the players can still follow those clues, and the characters can make skill checks, and when success is determined, they've found the tomb. The placement of the tomb may not have been determined ahead of time, or it could just be that the DM used the players actions and rolls to ensure they ended up where they needed to on a fixed map.
So the real question is, does it really matter? If the DM has a map, with hexes, and a specific hex divided into sub-hexes, and the tomb placed precisely ahead of time, is it better to let the PCs wander around for 5 sessions because they aren't quite getting it right? Or is it better to be less rigid in the design, and determine an appropriate time and potentially skill checks, etc. before arriving?
Nowadays, a more common approach is to avoid the exploration altogether, and narrate the journey.
The reality is that you can also blend these techniques, and I think that that's the approach that works best for me. If the PCs are searching for a tomb that's been lost for thousands of years, does it really need to be right
here? Why not over there? The important part isn't usually exactly where it is, but that the PCs actually find it. So a general placement (within these hills) is usually sufficient for me.