A GM’s rolls aren’t “against” the players they are merely the game mechanics in action. That is precisely why most rolls should be done in full view, so that the integrity of the roll is without question. As to your question on flexibility, the player would have to explain why a secret roll should be a known action or one that he or she is rolling. I’d ask a series of questions based on the situation: How does your character know for sure there is no trap vs he failed to find the trap? What if there is a modifier that the player is unaware of? ie it is a master crafter trap, installed by a Master Thief of the Thieves’ Guild so it is -20% to detect and -30% to disarm. I would roll the detection roll for the PC, apply the modifier, and if successful I’d then narrate “You have discovered a masterfully concealed trap and after closer inspection of the mechanism, you expect that disarming it will be an equally difficult task.” Then I’d wait to hear the PC explain how he might attempt to mitigate that challenge through roleplay (in character). “Yarra closely examines the trap, even shining a light source directly at it. He remains crouched down staring at the device, while he sorts through his various tools trying to select the best tool for the complex trap.” The other PCs notice the unusual amount of time Yarra is taking. The Dwarf, Tovid, who has some tinkering experience comes over to look at the device as well. GM - asks Tovid to make an INT or background skill check. If he succeeds, GM “You notice something about the device’s mechanism that could be helpful to Yarra”. The GM secretly reduces the difficulty of disarming the trap by 20% or based on system Yarra can roll with advantage his disarm trap skill. Any time a player wants to do something that is typically unknowable by the character, ask the player to roleplay it out in character and ask other characters to assist in what ways they might.