"But maybe their objection is that what's source for the goose is source for the gander. "
Unlike BT's network, Virgin and Cityfibre weren't built with masses of government money, and nor have they been expanded using massive government grants given for the purpose.
In any case all that's needed is an operational split and requirement to treat all players the same. Openreach can still stay as a for-profit company. The first thing it would do as a non-BT controlled outfit would be to make offers to provide service to Virgin/Cityfibre etc or buy them out to get access to _their_ ducts.