I think you're both right in a certain sense. The set of provable statements in intuitionist logic is a subset of what is provable in classical logic, which is what I believe the parent was referring to.
You're certainly right that any constructively provable statement is classically provable, that follows from intuitionism/constructivism generalizing classical logic. But I don't see how we could interpret the following to mean that.
> you can do intuitionist mathematics in classical mathematics