When you enter layout mode and make sure that Show | Sample Data is not selected in the View menu, does the field name start with the characters "::"?
That would indicate that the field comes from a table occurrence that is related to the current layout's table occurrence. If a related record exists, the field is editable. If such a related table does not exist, the field will not be editable until that related record is created.
A script trigger could also control access to a given field selectively such that the field is editable in one case and not in the other.
And a validation rule might allow you to enter data into a field, but reject your data and show an error message if it violates some validation rule set up in Field Options.
I checked the access privileges by going to the layout inspector and both the Browse Mode and Find Mode are checked in the Behavior section.
To avoid confusion, we usually refer to those as "field behavior settings". We refer to access privileges as limits controlled by settings inside Manage | Security. That's also possible here, but you'd get a message such as "your access privileges do not permit..." in that case.