Thanks for all those that chimed in.

Here is where I am at. Some of my original post was wrong.

Here is the bike with the bare rim:



Here are the tires that came with the rim:

A shot of the wheel spinning but the clearance is VERY close.


Here is my brand new 27 x 1- 1/8 tire and there is NO clearance:



This is another set of rims that I have and the are 23-622 tires. That tire size is supposed to have a 1995mm circumference.
Unfortunately the rear wheel is a fixie wheel so I'd need to switch the cassette from one rim to the other. Is that easy?

My 27 x1-1/8 (28-630) tire is is supposed to have a smaller circumference of 1978mm. yet these wheels do not fit... and the 23-622 wheels, with a larger circumference do fit.
Please explain that??

Here is a photo of the 23-622 wheel spinning and they have plenty of clearance: