For the greater good of role play is a fine way to DM, except...
Heavy stuff...but it shows that there different styles of how to handle dice as part of the game. In High School, I would play with a couple people as we walked between classes. No dice what so ever, just describe your action and the DM would let ofus know if it worked or not. IfIt was combat light, andwith more puzzle and exploration, but it was fun.
You mention, "As a DM I sometimes skip certain resolves..." So thatThat would normally be an indicator that you've already set a precedence that you don't rely solely on dice rolls. But it sounds like, at least to the player that is complaining, that you haven't made this well-known to your players, or that you didn't foreshadow this situation well enough.
Players need to be aware not just of the rules, but how you implement the rules so no one is caught off guard. Just like in High School, we knew that dice were not going to be used. But maybe theythe DM could have added a caveat about combat; "For combat, we need to use dice, so if there is an encounter, we need to wait until lunch so we have a table to roll on."