Even if this is true, it doesn't necessarily mean the economy's doing better. It's pretty likely that the job openings require skills that the newly unemployed workers do not have. Otherwise, they'd be filled. You can't hire a former real estate agent at Google and expect him to be immediately productive. (Hell, you usually can't hire a software engineer at Google and expect him to be immediately productive, but at least you can hire him.)
The issue with recessions is misallocation of capital, and it can't be fixed with a magic wand. You generally have to wait for people to retrain in new, productive areas of the economy, and for capital to be liquidated and entrepreneurs to find new uses for it. That's why it takes ~4 years instead of ~4 months.