Let's not make stuff up as we go along.  As the W-9 instructions state for single-owner disregarded entities, "You may use either your SSN or EIN (if you have one), but the IRS encourages you to use your SSN." Ironically, this is on the same Page (5) where IRS cautions that one way to "Secure Your Tax Records From Identity Theft" is to "Protect Your SSN."  

Many years ago the CP-2000 program could not link EIN's to SSN's.  IRS now has and uses that capability.  If my client has a choice between spreading an SSN promiscuously about the countryside, or using an EIN, I will advise protecting the SSN.  I don't care what IRS prefers: I no longer work for the government, I work for my clients.   You can tell your clients what you like, but let's at least recognize there is a choice.