Really where does it states that?
The only way I am sure that would increase ships building is for the tech only and the comes in the civilian research lab tier 6 or if you discover Relativest Factories (not sure if that is the name)
if you get either the research level of the tech or the artifact, it will increase the speed of building ships
I think what you are talking about is the starbase ability, where you could build ships, then yes
If you research tier 4 or 5 of the starbase ships building ability in tech (for sure) (rest I don't know) then research in starbase, up to level 2, then you get an increase of a certain percentage if you build from that starbase (I don't remember how much)
So since starbases upgrades can only be done by military labs, so in essence, you can increase ship production by using military labs and starbases