I don't think so. The sentence seems to be accepting the distinction between imagined pain and real pain, and saying that the imaginary nature of the former does not cause it to hurt less than the latter (technically leaving open the possibility that it does hurt less for some other reason).

Also, we clearly can distinguish imaginary pain from real pain. For example, there's a difference between the real pain I feel if I stub my toe and the imaginary pain I "feel" if I imagine myself stubbing my toe.

But a pragmatist in many people would say: “why then that person does not take any antidepressants/codeine?”, if that pain is so painful?

So it may be quite a bullshit statement, depending on how you take it.

We're just talking about cases where people suffer pain because of false beliefs, which can easily happen to people who have no mental health issues. If you heard that a loved one died, you'd be in a lot of pain, regardless of whether or not that report was true (so long as you believed it).

Bingo. You'd never say, "Oh thank the heavens they didn't die after all and so I was just imagining that pain!"