[jussij]

I might be wrong but I suspect the "schedular" in this instance is the thing granting write access.

Consider a SQL database engine.

Many threads/process can be accessing a SQL database at any given time.

But if two of those actors require write access to a same object, only one will be allowed access and all others are blocked.

So at this high level the concurrency is guaranteed by the engine, which then means at the low level the engine can safely assume the access is exclusive.