The criteria for it being a business purchase or not, is if the entity buying is a business or not and the purchase is for use by the business, not if the entity has a VAT number. For example, if my company was below the VAT registration threshold and therefore did not have a VAT number (and not be claiming VAT back as a result, so somewhat academic), it would still be a business purchase.
You can 100% make a business purchase and pay VAT. There are many cases where we make purchases from abroad where the seller does not have the facility to validate the VAT number through VIES at the point of sale, so it goes through with VAT paid then we reclaim it later.
