Sorry...but you are not entirely correct. Meat packers may sell to both Walmart and Krogers, but it is not the same quality.
In many cases Walmart will use a no roll beef ( ungraded) product and Krogers uses choice or select. If you look at pork you will find much of what Walmart uses is pumped with salt solution, soy etc.
Both Walmart and Kroger stores have gone to centralized cutting and a lot of the meat you see at a store was not cut at the store.
I would not buy ‘fresh’ meat at Walmart unless it was the only source available.
There are less than a handful of meat packers in the US now. Consolidation ran all the little guys out. The meat all comes from the same place, I used to sit for hours and watch it sold .
“Handling, temperatures, etc” are strictly enforced at all wholesale and retail outlets.
If you feel better paying more thinking you are getting a better product, go right ahead. Poor quality in the refrigerated section can be found at any retailer. Purchasing meat is like purchasing other fresh foods, a skilled buyer rarely buys poor quality.
Of all the meat sold, the only operation that has direct input to what they sell is MacDonalds. They have buyers that buy meat on the hoof and do their own processing. No grocery operation does this.