As stated - if sales tax is collected then they have to have a tax ID number. Tell them you need it for your accounting records. If they can't (or won't) produce one, pull out your phone and say, "That's okay. Let's just call the Tax Assessor's office and get the info from them." If they are BSing you, they'll back off.
Considering some people have mentioned getting letters from the IRS about income taxes due to "numerous sales" or a "hobby business", some people may just be covering their ass.
And of course, there are those few select people who follow every rule even if they don't have to. Might be some guy who always drives the speed limit, always has his hands at 10 and 2 on the steering wheel, and collects and submits sales tax revenue even when selling a broken lawnmower for $10....