"break in" is a slippery term, more often than not it's used to simply shift the time/labor to properly finish and mate parts from the manufacturer to the customer. You see it claimed all the time in the firearms industry when a gun doesn't function properly the customer is told to put 500-1000 rounds through it before sending it in. Basically the manufacturer is hoping the out of tolerance or poorly finished part(s) wear enough in those 500-1000 rounds that the gun works like it should have out of the box. In those cases it's simply an excuse for poor quality control and not putting the tolerances/effort into final finishing and fitting of the parts. With CRK I highly doubt that's the case, it appears something certainly is amiss with the knife beyond just a little high tolerance surface polishing/mating. There's a big difference between "break in" where high tolerance parts mate with some initial use going from smooth to super smooth and something that isn't functioning as intended.
I have noticed that a lot of grease similar to CRK's, Tetra, TW-25b etc. work amazing when "fresh" but tend to "gum up" quickly over the course of a few weeks/months. I've gone away from those lubes unless it's on an item I'm doing maintenance on frequently. So I'd give the knife a full tear down, inspection, and relube and see how it feels, it's possible it's just too much/old lube or a tight pivot, or a washer binding. If it still doesn't work right, or you don't want to mess with it, between KSF and CRK they will get you something you will be satisfied with.
I have noticed that a lot of grease similar to CRK's, Tetra, TW-25b etc. work amazing when "fresh" but tend to "gum up" quickly over the course of a few weeks/months. I've gone away from those lubes unless it's on an item I'm doing maintenance on frequently. So I'd give the knife a full tear down, inspection, and relube and see how it feels, it's possible it's just too much/old lube or a tight pivot, or a washer binding. If it still doesn't work right, or you don't want to mess with it, between KSF and CRK they will get you something you will be satisfied with.