The difference is that depending on Monty's algorithm, there is a different probability of getting the exact result we saw, namely seeing a goat. The exact event we actually saw happens with different probability depending on Monty's rule, so Monty's rule changes the meaning of that result.

The researchers don't get a given exact sequence of 100 results with different probability depending on their state of mind - their state of mind is not part of the state of the world that the result sequence tells us about, the way Monty's state of mind is part of the world that generates the exact goat.

To look at it another way, a spy watching Monty open doors and get goats would determine that Monty was deliberately avoiding the prize. Watching a researcher stop at 100 results doesn't tell you anything about whether the researcher planned to stop at 100 or after getting a certain number of successes. So, just like that result doesn't tell you anything about the researcher's state of mind, knowing about the researcher's state of mind doesn't tell you anything about the result.