This advice works in a surprisingly wide variety of situations. It's good to stick to principles and say "hell no!", but sometimes it's not worth a fight. It doesn't work with taxes, but certain problems just go away if you ignore it.

In situations like this, I put it on my long-term to-do list to get it off my mind. In a remarkable number of cases, I get to cross it off my list months later without having had any arguments.

That might not hold up in court. By showing up to work (and getting paid in return), there's an implicit contract.

I don't know enough about law (and neither do I know your jurisdiction), to say whether that implicit contract would include the non-compete they obviously wanted you to sign.

I'm sure you're right, but I think it would also be difficult for them to enforce if they couldn't produce a signed contract. If I were planning on, say, using trade secrets from my current employer to start a direct competitor stealing their biggest customers, then yeah I'm sure it wouldn't hold up in court - but I'm not going to do that. It's more a way for me to be able to honestly tell my next employer - who might be in the same ballpark industry, but probably not a direct competitor of my current employer - 'no, I did not sign a non-compete contract with them.'

That's really good advice! I'm going to use this one for sure.