No, you're misreading it. Information returns in most cases is the W-2 you send out to your employees and file a copy with the IRS for their information. I've always said that, for employment tax purposes, you use the LLC's EIN.

The entire quote on the IRS's webpage: "For example, if a disregarded entity LLC that is owned by an individual is required to provide a Form W-9, Request for Taxpayer Identification Number (TIN) and Certification, the W-9 should provide the owner’s SSN or EIN, not the LLC’s EIN.

For certain Employment Tax and Excise Tax requirements discussed below, the EIN of the LLC must be used. An LLC will need an EIN if it has any employees or if it will be required to file any of the excise tax forms listed below."

The original statement was SSN hiding for invoices, that's directly covered in the W-9 example. You can (have to) hide your SSN on W-2s, but not the W-9s you give to customers.