This is usually true, but there's a huge literature in economics about when it's true and when it isn't. Specifically, from a Keynesian viewpoint, in a recession caused by a stagnation of aggregate demand, government can create jobs without "crowding out" jobs in the private sector because, under those circumstances, the private sector was not operating at the PPF and those jobs were not going to be made.

Yes, but Keynesian recessions are a monetary phenomenon, caused by a shortfall in M*V (the quantity of money times its velocity of circulation). "Job creation" programs increase M*V (by increasing V), but they do so in an inefficient way; thus, they actually forgo some crowding in which would occur under more efficient policies.

I do broadly agree w/ the rest.