A five week old may not develop the signs of a stiff neck, headache, light sensitivity that older patients may demonstrated or be able to tell you about. Often they are only sick looking, irritable, and have a fever. The spinal tap was probably indicated in this infant and carries very little risk. It's odd that the family didn't consent. I don't think that the circumstances justified the subsequent actions however.
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.
Do you have children?
Glad you feel like its ok for outsiders to decide what is an acceptable risk.
Parents have the right to get a second opinion and take their child to another hospital/doctor. I am sure they weren't just going to take their daughter home and watch her suffer... they seemed proactive and would have taken her to a different facility for a second opinion... they were not given that opportunity in this case.