What's to stop a business from lying about its sales to not pay the sales tax it collected?

There's nothing actually preventing someone from doing that other than the threat of a heavy fine and jail time. The business might get subjected to an audit. The state will review the books adding up what items were bought from suppliers and compare that to what was sold. If the numbers don't agree you get charged what you owe plus a significant penalty and interest. Jail time is a possibility but that rarely happens. The audit can go back quite a few years depending on which state you do business in.

if you are the buyer, why does it matter to you what the seller does? and how would you know what they do ro don't do? by letter of the law - if they DON'T charge you sales tax - YOU are required to send teh tax to teh state yourself. woudl YOU actually do that if that was the case?

The possibility of getting caught and sent to prison.

Nothing but honesty.