Winchesters premium stuff (usually a black box) is fine. Their cheaper ammo (usually a white box) has a track record of a lot of issues. There was a thread about 9mm white box ammo that had cartridge overall lengths varying up to 1/4" in the same box. One theory that seemed to have traction was every so often a box of factory rejects would accidentally get put out with the good ammo.
Winchester unprimed brass cases are also prone for being dinged, dented, and often short one round in a bag.
I haven't found this to be the case at all. I have an old Cooey with a loose chamber and Winchester ammo regularly splits upon firing. Federal and CCI ammo work just fine (I believe CCI makes Federal rimfire ammo.)
Your old Cooey, has likely not been match tuned and was made to fire the hard primer rims that were so prevalent back in the day of its manufacture. I doubt that rifle will have trouble making any rf ammo go bang.
For some of us older fellows here, some of you must remember the heavily greased, black lacquer, Russian surplus 22lrrf that came in the big 2500 round sardine cans for $8. The cases were made of steel and loaded with lead bullets. The whole cartridge was stained black and slathered in lubricant.
The priming rim on these cases was hard as they come. Many pistols of the time, wouldn't consistently shoot them. To bad, because they were hellishly accurate.
My Cooey's loved them, all except for the damnable model 64 with the self destructing plastic mags, that were ahead of their time and not intended for extended use.
I had a S&W tuned target revolver at that time and was very disappointed when the Russian ammo wouldn't fire in it. I soon found out how important a hammer spring or firing pin spring is to positive ignition.
Recently, a friend of mine bought a lovely tuned, double action only S&W 38spl from me. I warned him that the pistol was primer fussy and that he should use match grade primers. Not much later, trying to save a few pennies, he loaded up some fine looking ammo, with what I suspect, were WW small pistol primers. Even at the maximum adjustment, many refused to go bang.