It does not have an actual Kreiger barrel,it has a barrel made by Criterion,which is a company owned by Kreiger.Weatherby used the Kreiger name in it's advertising in the hope that people would assume that their rifles used actual Kreiger barrels.
Correct in that they are not the same as the custom barrels that Krieger is well know for. Weatherby advertises their barrels correctly as a Krieger Criterion button rifled. The Criterion barrel is still a Krieger barrel. A comparison would be saying that you have a Chevy but not a GM.
One of my brother in laws has a Krieger custom barrel on a gun he had made for him. I don’t think the Criterion barrels are made in the same plant any longer. I spoke to a tech at Krieger a few months ago when I was injuring about a barrel for my new Sako 75 and I thought he said they were in a different building. Never the less, the Mark V barrels benefit from Krieger’s barrel manufacturing expertise even though their rifling processes are different.
The name of the Mark V action manufacturer slips me now but, I think I have it written down somewhere.