You are answering your own question: companies collect VAT from consumers and pass it on to tax authorities.

Then, as the company is VAT-registered what it purchases is either VAT-free or VAT paid can be deducted from the amount of VAT collected from consumers (as you said).

Bottom line: companies do not pay VAT on their own purchases, they only pass on VAT collected from consumers.

Obviously companies do make actual payments to the tax authorities but the point is that these are not from their own funds, they only effectively act as tax collectors.