I think it's pretty clear if it is not stamped "Begara," it's not a Begara barrel. As MD noted from the CVA website:

"Every barrel that we use today is also made in Bergara at our BERGARA BARRELS facility, which, like CVA, is wholly owned by our parent company. "

That DOES NOT mean that all barrels coming out of the Begara plant get to be considered worthy of being called "Begara." There is more the brand name than what factory makes the product. Again, as others noted, Begara barrels are subject to extra steps with regard to polish/finish. I don't know all the steps/inspections/tolerences that are required to be worthy of the Begara stamp but clearly not all the CVA barrels get them, otherwise, they would all have the stamp.

Seiko make Pulsar watches, doesn't mean Pulsar watches are Seikos. Last I heard, Bushnell makes Simmons scopes (same manufacturing plant) and it's clearly a different product.

Word games? Maybe. But they are distinctions.