Does it make any sense to compute p-values for prediction intervals?

I received this email today:

My team recently used some techniques found in your writings to perform forecasts … Our work has been well received by reviewers, but one commenter asked two questions that I was hoping you may be able to provide insight on.

First, they wanted to know if we could provide P-values for our prediction intervals. In our work, we said, “Observed rates were …