Did Big Box lie to me?

My question is this - Is it problematic/difficult to recast a 14k white gold ring and reuse the gold?

I ask because the big box jeweler assures me that is what happened, but Google and local jewelers are telling me that would be problematic to do and is not recommended.

Backstory if you care to read:

I’ve had my matching wedding set since 2011. It is my original set and I never intended to upgrade or change anything about it. A small diamond fell out of the band. While the big box retailer was repairing it, the “apprentice” who was working on it damaged it beyond repair.

They offered to recast the engagement ring (wedding band wasn’t damaged). I am very sentimental and the idea of a new ring, even if it looked the same, was killing me. That ring has been on my finger through it ALL. I never even removed it during pregnancies. I asked if they could use the same metal and they said yes they could.

The big box store shipped it off to one of their vendors and three months later it was finished. The problem is that the band on the new ring is now larger than the wedding band. They no longer match and I won’t settle to just live with it like that.

I don’t want the wedding ring recast to match because I don’t like the thicker bands. I have small features, ring size 3.75, and I only want delicate dainty bands (like my original set). In addition, my diamond isn’t quite a carat, and now it appears much smaller because of the larger band.

Anyway, I’m trying to figure out how to keep these rings as close to their original state, because again, I’m sentimental. I’m thinking of just paying a local jeweler to recast the engagement ring back to its original band size, but am told they would not re-use the metal.

This has me wondering if the big box vendor who did the original recast truly used my metal or if it was just a lie (how would I ever truly know?)

Pics of original wedding band and the new recast engagement ring.