Independent contractor situations are contractual arrangements. The contract may be oral; no law requires that it be written. The problem with an oral contracts for personal services is not that oral contracts are invalid, just that it is harder to prove the terms of the deal in court with an oral contract.
The person or entity that hired you should have got your W-9 information in order to complete the Form 1099s that it must file. It does not have to use the Form W-9; if it has the needed information some other way that’s fine. There are some risks not using a W-9 and getting the information some other way, but that's for the employing person to decide how to get the information. In any event, the failure to have you fill out a W-9 does not by itself mean you are not an independent contractor (IC).
The focus of the independent contractor determination is looking at the degree of control you have over how, when, and where you perform the work. The more control you have over the details of the work you do the more likely it is that you are an IC.

