Yeah, they should have permitted it, but the doctor should not have called the police unless there was a higher likelihood of a problem. He just misjudged.
I don't think I'd agree... my daughter went into an emergency room with 105* temp at age 4 and after treating her for an hour, my wife called me in and said the doctor wanted to do the spinal to rule out meningitis! I took my wife out of the room and told her OVER MY DEAD BODY! This is called practicing defensive medicine on your fat insurance coverage... no tap, got her out of the hosp ASAP and monitored her vitals for two days, and she completely recovered. No thought on the dr.'s part of the trauma and discomfort of the procedure etc... YOU are in charge of your children's care and it's your responsibility to step up and keep unnecessary intrusive stuff away from your kids!
Good luck next time you step into a facility where you don't know the history, background or competance of politically correct med school grads...