Disclaimer: Any opinions expressed, potshots taken, or scientific views articulated are mine, and need not represent the opinions, potshots, or scientific views of the Federal Reserve Bank of St. Louis, or the Federal Reserve System.
I kinda wished they had included a model but it seems pretty clear that they're thinking through the lens of something like an RBC model+MP search and matching labor market. I've always liked the approach, it gets rid of the "unemployment=taking a vacation" argument against real business cycles. Your St. Louis Fed/blogger colleague was one of the first to do it if I recall correctly.
Yes, Andolfatto was well before his time in that respect. Monika Merz did related work at the same time.