I've always thought this was a pretty terrible excuse. Not the paramedics' fault, but more the call handling / dispatch system.Had to go to the hospital last year in an ambulance and chatting to the paramedics they often have people calling 999 and ambulances for stupid things like stubbed toes, sprains and the like. They do a great job under difficult conditions.
I get that some people lie about being seriously injured when they aren't just to get an ambulance out or whatever and you can't really do much about that. However some people ring up and tell the truth about what s happened. If 999 (or more likely 111) decide to send an ambulance for someone with a minor injury then that's on them. Simple answer is that if someone rings up with an injury that doesn't need an ambulance then don't send them one. Tell them to get the bus or a taxi to the nearest urgent care centre.