To explicate this part, as I understand it: Only the final customer is responsible for the VAT, so at every intermediate step in production the business takes a tax credit to offset the tax they're paying.
This means there's no good way to cheat, because every firm is filing paperwork about every link in the production chain.
(Perhaps not important for a product manufactured abroad, but interesting!)
Basically, yeah.
When I buy something through my company, I don't pay VAT up front. That business transfers the responsibility to pay VAT to me (they include this in their tax statements), essentially deducting it from their own taxes.
If I bought goods with VAT included and use them for my business, I'll register the VAT separately.
Then, when I sell something to a non-business customer, I offset the price I want to charge with the VAT over that full price. (Often fudging with that non-VAT price a bit to get a nicer-looking with-VAT price.)
And at the end of the quarter, I pay VAT over my income (before expenses, and including that offset price from earlier), minus any VAT I paid earlier, and in doing so, cover the VAT for the other companies I bought things from.
If I somehow didn't have any income, I still have to pay all VAT from the businesses that transferred that responsibility to me.* But this is deducted from my VAT next time I do have an income. (And there's ways to delay payment if I were in really dire straits.)
(There's more complicated scenarios when dealing with different VAT rate categories, or having paid VAT for something in a different country, or buying something that's not fully for business use, or something where VAT is spread over/offset to different periods, but that's the gist of it.)
*And if I bought a bunch of things through my company but don't pay any VAT, despite those other companies having offset the responsibility to me, I'm the one who gets in trouble. (Likewise, if a company claims to pay VAT over something I buy but doesn't, I can still deduct that VAT from my VAT payment, and the company that didn't pay VAT gets in trouble.)