The count is PU's responsibility. When I'm BU and asked by a base coach or player for the count, I refer them to the PU. I keep track of the count for my own purposes, but I could be wrong. I don't need a base coach up my butt because he gave instructions to his runners based on incorrect information from me.
Some umpires do not carry an indicator on the bases. I do not. It's not too difficult to remember three numbers. Some feel it looks ridiculous for the BU to be staring at his indicator between pitches and that he may be distracted from what he should be doing...watching the ball.
In most areas I've worked, the sign used to confirm the count is the twirling of the left and right hand index fingers in front of the body.
I have run into the attitude you describe. At my first D-1 game many years ago, on the way to the field my crew chief asked to see my indicator. I handed it to him and he chucked it about 50 yards and said "thanks." I got the message.