If THIS confuses you, I have a long list of movies that you should never see, mainly, most movies.
Yes, you got it right at the very end. The doctor discovered that mamma had a deadly disease which could easily be spread and caught. Just the news of it could cause a lot of distress. So, the government health dept (or whoever) decided to just make the mother disappear as if she had never been there.
You ask if we agree with him? I not sure if you mean agree with that decision or agree with you about the conclusion. So I will answer both. No, I don't agree that the situation should have been handled that way and, Yes, I agree that it was about 'The old woman had a contagious disease. They set it up to prevent a panic'.
It seemed pretty straight forward to me.
mf
Trust me. Im The Doctor.