Just because the customer assures the seller that they'll pay the tax doesn't relieve the seller of any burden to collect the tax. But, if the buyer provides the vendor with a direct pay certificate, that'll work.
In most states, there is a recognition that some buyers have such complex purchasing situations that it would be easier to simply let them self-assess the use taxes. However, most states are also strict about who they hand direct pay permits to. Here are the usual criteria:
1. Have good policies and procedures in place to make sure the taxes are properly self-assessed
2. Meet certain volume requirements
3. Go through an initial, detailed audit
4. Go through future audits almost every year.
Once the customer is authorized, they send their vendors direct pay certificates which the seller can then treat just like a resale or other exemption certificate (there are some restrictions). But without that specific piece of paper, do not accept the customers assurances that they'll pay their own taxes, even if it comes in a letter, contract, sales agreement, or PO.
In order to be relieved of your responsibility for collecting the tax, you need a direct pay certificate.
If someone said they're buying for retail, you wouldn't take their word for it. You'd want the resale certificate. Right? Right?
Sales Tax Guy