Any variable, or object, only supports a finite set of operations. Making a global object (and controlling access to its internals) versus making data global does not change that.
Controlling simultaneous access to a global resource from multiple threads, in itself, increases complexity. Of the functions controlling that access, at the least.
One common trap with multithreaded programming - which novices invariably run afoul of, without realising it - is that no object can protect itself from concurrent access. Something else (an object or a function at a higher level of abstraction) must protect the object.
That is not true. It is true that the presence of global data, in itself, increases the complexity of code that interacts with that global data. Or it increases the amount of analysis to put bounds on what state the global data is in, at any point in time.
The most complex programs I have seen did not have any global data (and, no, they did not use dynamic memory allocation after completing their startup/initialisation). Their complexity would have been increased, and their maintainability made more difficult, if they had made use of global data.
In a professional setting, whenever I have seen folks use an argument like that, I ask them to describe the architecture of their code. And I have only ever found one person making such a claim who could actually describe their architecture.
I see it more in amateur settings (such as people doing homework exercises). In an amateur setting I'll concede that simple programs can sometimes be made simpler by using global data rather than passing arguments. However, that principle does not scale to large programs.
Yes, it may take more typing to pass arguments to a function, or to specify data structures that can be used to supply non-trivial data as an argument to a function. But it is also harder to get a complex program running correctly when multiple functions make use of global data.
Data is global if it pertains to the whole program. Or it is not. There is no intermediate concept. So it is not possible for a variable to be "less global" than another variable.