You are correct.
I work at a shop and we had a debate going among two sellers if we can use the verb to fetch after the verb to go. When one said "My worker went to fetch your jacket", another one said that you can not use "went" if you use "fetch", you must say "My worker is fetching your jacket" because "to fetch" already means "to go and get it" so you can't use "to go" in front of "to fetch". I think you can say "He went to fetch the jacket" and it is correct. Please confirm if I'm right. We have a bet going on here.
I don't have a problem with the sentence. "Went to fetch" seems much more natural than "is fetching."