For me, up to that point when he entered that room, Brett believed that he was hunting for a small creature. However, upon further reflection, I agree with you that he acted stupidly when, after finding the shedded skin, instead of reporting his discovery to the crew, Brett decided to proceed further into the room, and placed himself in greater danger. Another moment that can be argued for a case of stupidity is when the captain went alone into the vents without a partner. So, in conclusion, I retract what I said earlier about the first movie.
What is far more stupid, is that Ripley and Parker force Bret to go by himself into the next room, where they can't see him or help him, to get the cat. Nor do they work as a group of three so that no one is alone. This kind of thing is repeated in the air shaft and at the end of the film when Lampert n' Parker seperate from Ripley. But this is your basic horror fare.