you said the details that arty could not fire the turn it was built/upgraded with that upgrade were logical and not needed. I don't think it is possible to see this however, from just the manual.
from my point of view, you can
1. build arty
2. bombard
from your point of view, you can
1. bombard
2. build arty
since there is nothing that says it's one or the other, i can't assume one or the other. However, the manual says artillery level 'a' can attack level 'b' cities distance 'c' away. So there is no fault with my building arty and using it at the same turn.