OK, found the issue - has taken ages, so hope this is helpful.
brianrich46, in his post of Sept 10 2013, tells us
"It appears that duplicating the [Read-Only Access] privilege set does NOT give you a new set with the same privileges, as users of the duplicate set cannot edit global fields by default, something they can do if they are using the [Read-Only Access] set."
...So if we want to tweak the default [Read-Only Access] Privilege set, we need to specifically allow access to any Global fields that may be involved in the UI - these will be changeable in the default [Read-Only Access] but not in any copy of it.
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Just one other annoyance in here, if you forget....
Not only do you have to set the appropriate Global field as modifiable under Records... this field also needs to be modifiable under Layout......