No, you must pay VAT on intra-EU B2B transactions too. The accounting is more complicated because the buyer pays rather than the seller, but it is still there.
And the accounting is there because of tax fraud, I guess. And I also guess that the US has a similar accounting system where they have to report the amount purchased per tax bracket and the IDs of the companies they bought from.
If I have misinterpreted it, I would very much like to know so I can inform my accountant. VAT is enough of a hairy mess as it is.