To be honest, I had never even considered the come/go question, but it could well be right. Initially I thought that reported speech would stick closely to the original words, but the first example I thought of was this:
He said "Would you like to come to the cinema with me?"
He asked me if I would like to go to the cinema with him.
I think the reason for the change in this particular context is that the first sentence is from his point of view, in which case "come" would be appropriate for him, but in the reported speech it is from your point of view, where "go" would fit better.
Student or Learner