Oh, I see now what your saying. Your diagram does not use a neutral and your saying yours is wired to a neutral not ground.So, follow up to @kok328 's comment...
If this ok with the Stat ground going to the neutral or should it come apart, cap the neutral and reconnect to ground?
Yes, this is incorrect especially off a sub-panel where the neutral and ground are not connected together as they would be in a Main panel.
Hate to change something that's been working but, yea, I'd connect the stat to ground per the diagram.