In science today I would think that looking at all possibilities is exactly the sort of advice I think one should give to people.
First, there are two key differences between what you wrote and EOM wrote. EOM said we MUST look at all possibilities. You wrote that people should be ALLOWED to look at all possibilities. Those are fundamentally different statements.
To negate the statement one end up with the suggestion that one should not look at some possibilities; however if we are really to take this suggestion seriously, we cannot decide to look or not to look at a possibility by investigating it's properties, because that would exactly require us to look at it in the first place
That's not true at all. No one ever said "don't investigate". The statement by EOM was "look at all possibilities". If a ball sitting on a table moves at a certain time of day, there are a variety of things I can do to determine why that is. What I don't have to do is entertain nonsensical possibilities, such as a butterfly flapping it's wings on Mars is the cause.
Saying "you don't have to consider non-sense or extremely unlikely possibilities" isn't the same as saying "don't investigate", much like saying "must" isn't the same as "allow".