I think the theory is that it won't do much good to just dig if the soil is too wet to drop off your spade. I have a similar problem in our garden which I have just redesigned to get rid of 2/3rds of the lawn and introduce some raised beds. The bits where the old lawn was were dug over in the late autumn but are now flat and waterlogged again (no wonder there was so much moss on the lawn). I have just taken delivery of a load of very coarse (woody) compost from our council and have thrown this onto my raised-bed and flower-bed areas with a view to digging it in as soon as the weather dries a bit. I don't think there's much point trying to dig wet soil as (a) it's hard going and (b) because you are standing on it you are driving the air out of it which is the opposite of what you want to achieve.
I'm going to follow up by digging some well rotted farmyard manure in to replace the nitrogen I expect the woody compost will grab, and I'll also get some chicken manure and have a go at recomposting some of the woodier stuff.
To dig or not is always a tricky question imo. If you work full time like me you sometimes just have to bite the bullet and get your spade out at the weekend come what may, but if you can catch the soil just right it's a lot easier.