This is false. If it was true, faucets would always be earning money, being that their spending is relative to the visitors, but the advertising money would be as well (such that 10 visitors would be just as profitable as 100000 visitors on a relative basis).
Let's try this another way.
Your advertiser pays $1000 for 1000 visitors. Your faucet pays $1 per visitor. You're breaking even.
Next month, you have 10000 visitors. Your advertiser is now paying $10000. Your faucet is now paying $10000.
You are at the same level regardless. They don't say "well, your traffic is 2x as much so we're going to give you 5x as much money." They will pay you relative to the traffic increase. If your traffic went up 2x, you would make 2x as much. You would also be paying out 2x as much.
If your site is not profitable with 100 visitors, it won't be with 10 million either.