Am I legally required to fill out a W9 if I was never a contractor, or a employee of the company requesting it?

A company may request your form W-9 for a variety of reasons.

Please read the instructions for form W-9, especially the paragraph on Purpose of Form:

https://www.irs.gov/pub/irs-pdf/fw9.pdf

A company can only request you to fill out form W-9 if they need to file an information return on you (form 1099 or 1098).

If you do not fall in any of the categories listed in the instructions for form W-9, you are not required to provide that form.

What happens when the contractor refuses to provide a w9 and we accidentally paid them already? 

Well, stop doing business with them until you get them to fill out a W9. Hopefully, the amount you paid them is not too large. But if you have their company details, like their EIN on file, you can use it too to issue them a 1099 Misc.