Lisa, I haven't read Harris Coulter's books, but I am a living example of what you cite.
I had the single vaccines as an infant.
Age 5 there was mumps going around and it only came out partially in me, and I am told I was never the same again.
Age 13 I contracted measles which damaged my visual acuity significantly.

I conclude, at least for myself that:

1. vaccines do not give immunity
2. diseases which are normally transient acute episodes, can cause lasting harm if they are adapted by vaccination.

I also personally met a child who is autistic (without speech) since the day of MMR vaccine, who had normal development including speech, up to that day.

Today there is a report on the news about an outbreak of measles in an area of London in which uptake of the MMR has fallen to 65%.
A parent was interviewed who said their child got the complication of pneumonia with measles which "almost reached the brain". They went on to say that they hadn't had this child vaccinated because they didn't have enough information about safety, but as soon as she was recovered they planned to have her vaccinated.

I hope the reporters will interview some parents who say "I don't know what all the fuss was about - it was a simple disease" - but then that's not news...