[physicsguy]

No, if you provide a VAT number, in business to business transactions, companies will not normally charge VAT in the first place, so you don't pay it when you purchase in many cases as a business.

However if you go into something aimed at consumers, and make a purchase, they're normally not set up for this, which is why you're able to reclaim when you have paid it.

[AnAfrican]

This may be an arrangement set up in some jurisdictions and probably widely used nowadays.

The default (as in « the original setup ») is what i’ve described.