The problem I have with umpires who say "no catch" is that doing so can also create confusion. They may not hear the "no" part and think you yelled "catch." That's also why you never hear them say "fair ball." On a trapped ball, make the proper trapped signal (in ASA, it's the same signal as "safe"), and let the players figure it out. Sometimes, I hold onto the signal a second or two longer than I normally would, just in case there's confusion. If a coach gets upset about confusion on the field over something like this, they have no one to blame but themselves for bad coaching.
I've seen exactly what you've described happen dozens and dozens of times on the field. Balls that hit the ground that players thought were caught, infield flies that an infielder didn't catch, and fair balls deep down the line. Let the play unfold and sort out the mess when progress has stopped.
