Forgive my ignorance here, but isn't it simply better for the economy to have low rather than high unemployment? And since a recession is basically "the economy is doing bad" doesn't that mean that the unemployment argument is: "it may be doing bad, but not /that/ bad". And then the discussion is if the economy is doing bad enough to call it a recession, people point to low unemployment and say: no.
There is a lot going on in this question, so I apologize if my answer doesn't address.
It really comes down to what you mean by "better for the economy". When most people care about the economy, what they really care about is how much "stuff" they or the average person can buy.
To one extreme, many people would still be unhappy if the GDP and "economy" doubled, but only 10% of people were working. Either 90% of people would be going without, or they would be on some sort of welfare taxed from the 10%.
To the other extreme, many people would be unhappy if there were 100% employment, but all you could buy with it is a loaf of bread.
The ideal is to have high labor demand (usually associated with high employment) and growing GDP.
This means that people who want to work can easily get a job, and the amount of "stuff" they can get from working keeps going up.
