This raises another question: how close is closely? A gnat’s behind or rodents’ whisker? Bottom line: Anything less than Uncirculated is AU. Some coins show no wear but still grade AU due to poor handling, like excess contact marks or coin-to-coin abrasion.
Back in my data processing days you had to be very precise when printing payroll checks. Checks that were out of alignment had to be destroyed and payroll run again requiring all kinds of documentation. Needless to say we made sure that everything lined up perfectly. We didn't use a rodent's whisker or a gnat's behind as a unit of measurement, for us Boston University yahoos the favored unit of measurement was a pubic hair.
There's one eBay seller that's been using "closely uncirculated" for a while, and I've seen some Chinese fakers start to copy the term.