Hans' answer, combined with Albert's post that lists the consecutive Brunswick/Vocalion matrix numbers for sessions that took place in the middle of June 1928, seems to conclusively prove that Benny's "Clarinetitis" session indeed took place in Chicago in June 1928, when Benny visited there while playing a pick-up job with Sam Lanin. It appears my earlier guess was wrong.
I also noticed that the Vocalion catalog number for Jack Pettis' recording of "Dry Martini" and "Hot Heels" (June 20, 1928) is 15703, while the Vocalion catalog number for "Clarinetitis" and "That's A Plenty" is 15705, which seems to be more evidence that these recordings were cut and issued at roughly the same time.
Perhaps it was company policy for Vocalion items to all be issued with a NYC matrix number?
One more thing -- I own a French Brunswick release of "Clarinetitis" (coupled with "Blue" by Bennie Goodman's Boys). The FrBr issue of "Clarinetitis" bears the Melotone catalog number M12073 on its label, and the NYC matrix E7397 in the wax near the runoff grove. But according to the Ross Laird discography, Melotone M12073 was issued with the Chicago matrix number C2005. So much for consistency!