Do I need to fill out a W-9 form if I'm not getting paid?

I'm a private music instructor who works with several other instructors in a private studio. My students pay me directly, writing checks out to my name, or paying me in cash or via credit card payments which I take with my iPhone. I pay the studio owners a set amount of rent per student, and over the past 8 years we have all been happy with this very informal arrangement without resorting to any type of contract outside of a verbal agreement. I file my own taxes, and report the income I make as a teacher as self-employment, I do not receive any payment from the studio in any way. Recently my associates have approached me and demanded that I provide them with a W-9 form, insisting that I have to fill it out to prove that I'm a citizen legally able to work in the United States in accordance with their incorporated status. My reasoning for denying them a W-9 form is that I'm not an employee, and do not receive any payment or wages from their corporation, and am therefore not liable to them for any sort of tax culpability.Am i correct in assuming this, or are they correct?

And the requester more than likely does have a valid reason for asking you to fill out the W-9 form and return it to them at this time in your life for this purpose.
How Do I Know When To Use Form W-9?
Use Form W-9 to request the taxpayer identification number (TIN) of a US Person (including a resident alien) and to request certain certifications and claims for exemption. (See Purpose of Form on Form W-9.) Withholding agents may require signed Forms W-9 from US Exempt recipients to overcome any presumptions of foreign status. For federal purposes, a US Person includes but is not limited to:

http://www.irs.gov/...html#d0e58

Hope that you find the above enclosed information useful. 07/11/2012

You are wrong. A W9 is similar to a W4 but for independent contractors or other special categories. It is usually needed if they pay you. It is a protection from them and nowadays things are getting more and more regulated. I do not see any reason not to give it to them.

"I pay the studio owners a set amount of rent per student"

It sounds to me like the studio is undergoing a payroll audit. The IRS has ruled many times that "rent" has to be set by day, week or month, not by client.

What they want is an I 9, not a W-9

They shouldn't need a W-9, but do need the I-9.

A W-9 form would not prove that you are a citizen legally able to work in the United States.

The form to do that is an I-9 form, not a W-9 form.