You are not supposed to use the EIN of the disregarded entity. The W-9 is an income tax form and the entity is disregarded for income tax purposes. The reason for a disregarded entity to get an EIN is if it has payroll. The entity is not disregarded for payroll.
The number on the W-9 should be the SSN or EIN of the owner of a disregarded entity. If you do not want to give out your social security number, you should get an EIN in your name as a sole proprietor. That is what footnote three is referring to.
