I don't believe this to be true. We have business interests in Canada which has a 7% GST (Essentially a VAT). Here's how it works:
Jim cuts down an oak tree from his woodlot and sells it to a mill for $1,000 + $70 GST. He deducts $40 to cover GST he has paid on his truck, chainsaw etc. and remits $30
The mill cuts the lumber and sells the boards to a furniture company for $2,000 + $140 GST. It deducts the $70 GST it has already paid and remits $70
The furniture company manufactures several dining room suites with the wood, and sells it direct to consumers for a total of $4,000 plus $280 GST. It deducts the $140 GST it has paid on the wood, and remits $140.
So the government gets a total of $140 (from furniture mfr) + $70 (from lumber mill) + $30 (from Jim) + $40 (from Jim's suppliers, truck, chainsaw etc) = $280.
So the government gets only the $280 total--it's not multiplied.
There are advantages to this for business if it replaces income tax. Goods coming into the country have VAT applied at the border. So US business can compete on a level playing field with lower taxed foreign competitors.
Remember that US business are burdened by three tax disadvantages.
1) A corporate tax rate that is no. 3 in the world, soon to be no. 1 as the two higher european countries are planning on lowering their rates.
2) A tax on worldwide profits. The US is, I believe, the only industrialized nation to do this. US firms operating overseas must pay taxes in the foreign jurisdiction as well as to the IRS. In some cases, tax treaties reduce double taxation.
3) Double taxation on dividends, which halves the attractiveness to investors of companies which have a great ongoing business which is not high-growth (i.e. no capital gains).
Note that this is a simplified example since the furniture company would also get to deduct GST paid on machinery and supplies.