Lying about real estate price

[George Goldstein]

You know how when you buy a used car from a private seller you tell the seller to say he sold it for $3000 instead of $18000 so your dmv tax is lower? What prevents you from doing the same for real estate property taxes?
For example, you buy a house for $1,000,000 but you say you bought it for $100,000
How do they find out how much you paid for a house to assess their tax? If buyer's story matches seller's story, how do they find out? Are they going to flag it as a statistical abnormality and send investigators after you?

Another way that I can think of is let's say I want to buy a house. My friend buys it for $1,000,000 and then sells it to me for $100,000
why don't people do this? sounds completely legal, maybe my friend is crazy and he wants to lose $900,000