Yes, VAT is tax on revenue
of the entire supply chain as a whole (not individual companies), so long as it is within a group of countries using VAT.
But it didn't look to me like that's what the GP comment meant. I assumed they meant tax on revenue taken by each company. No need to account for expenses...
I'd hoped that would be obvious from my comment, but if not I hope I've clarified that now.
ps. It looks like other commenters here are confused about this language, and arguing over the semantics of what "tax on revenue" means.
VAT doesn't solve all tax fairness problems unfortunately, which is a shame because it's a fairly well administered system, and good at catching fraud.
There are good reasons why VAT is not the only tax on businesses. One of those reasons is that immediate revenue and expenses are a poor model of many business accounts. Accountants use more sophisticated models (there are professional standards they have to adhere to), and despite their quirks and loopholes, these are generally better, fairer, more representative models of the state and value of a business and the money flowing through it, and as a result, for most "ordinary" businesses (i.e. not international corps gaming the system heavily), that ends up making taxation fairer.
Someone mentioned using a higher rate for higher revenue. That suggests an example where the better models which incorporate time and stored value results in fairer, more appropriate taxation. If you have a higher sustained revenue, year on year, it makes sense to use the higher rate if that's the policy. But if you make zero in year $X and twice your normal in year $X+1, then back to normal in years $X+2..., all just because you had a big customer pay late for the first year, fairness says you ought to end up paying the appropriate tax rate for your steady normal in the long run, not twice as much tax thanks to your late-paying customer!
The accountants' model handles that just fine, as it says you earned the money fair and square in year $X even though you didn't get paid that year. And that's generally better for limiting tax avoidance too, because it reduces the ways in which co-operating companies can game the system by timing their payments to each other to cheat. (VAT doesn't show this problem because it's a fixed percentage, but it occurs with progressive taxes, meaning variable percentage.)