Ok,

We are containing / solving the issue.

Yes, DAT 5958 is faulty and is producing false positive, specifically for service.exe.

Should anybody need help, I'll post here the solution we are adopting, even step by step if you need. We are simply reverting manually, one machine at the time, to 5857 . Which is not easy as not all machines allow you to logon easily.
Meanwhile, McAfee has released 5959 which seems to work.

It seems to me that McAfee is, in their official statements so far, minimizing the problem. In our three main locations, NY, Rome, Paris, we were badly hit. Yesterday it was no fan at all.
I know for sure that other organizations in Paris have been badly hit. I know for sure other organizations in Rome are being badly hit. We are talking about hundreds of workstations, here, only for us. I don't know where McAfee data is coming from...