Question about markings

[gforz36]

I have a watch from my grandfather, who died in 1974. It's been sitting in a case since that time. It is not running.
It appears to be a Rolex, but its markings puzzle me. I've done a little homework on the basics of it and it would appear that he would have gotten this sometime in the late 1950's or 1960's. I don't know if fakes were prevalent during this time, but my grandfather and grandmother didn't shop at flea markets or pick up stuff on the streets.
Here's the rub: It is a Rolex perpetual Day-Date, except underneath where it says oyster perpetual it says Date-Day and not Day-Date. There is also no coronet above it, and it doesn't say "Swiss" on it at 6pm. It has a gold pie-dish casing with fluted gold bezel, flat tipped hour and minute hands and a second hand, and lume dots at the base of each hour tick, Roman numerals at the end of each tick. Cyclops bubble over the date window. There's a coronet on the wind, no marking on the back, band is stainless steel with 3 link-wide strip of what appears to be gold.
I've googled the heck out of this, and it looks like it needs to say Swiss or Swiss made on it to be a Rolex, but I thought there might be an old model that they didn't put it on. Unusual where it would have combination of no coronet on dial, saying Date-Day whereas most of the rest say Day-Date, and doesn't say Swiss on it either.
Any ideas??

[JEC]

This will require pictures. Have you opened it to check the movement? Also remove the band to check model and serial numbers. It should be a solid gold case, not plated.