I wanted to update this, as it took me a little while to come up with the solution.
Let me clarify some details, as perhaps I wasn't as clear as I could have been in my initial post.
1.) I am trying to pull a text field from one window in a process to another window, as read-only.
2.) The text field I am trying to pull is NOT on the core object (problem, change, incident etc.)
3.) Creating a relationship between the two objects and pulling data back and forth does not work, even if you have the top-level object on the window.
4.) Note that this will pull the LATEST field from that attribute by default.
What does work
In order to get an attribute from one collection, to display as read-only on another collection window, you need to use a copy rule.
1.) Create a text attribute on the core object, call it something you can remember.
2.) Create a copy rule on the core object that pulls from the field you want, to the new attribute you created
3.) On the destination window, make sure that BOTH the core object and the attribute you want are on the window.
4.) When the page loads, the copy rule should have fired with the LATEST entry, and you will get your text displayed as desired.
The reason this was difficult for me, is because I didn't realize that the core (parent) object was needed. I assumed you could have relationships between any objects and have copy rules fire back n' forth.