The VFR corridor the controller was referring to was indeed the section of airspace directly above KMSY heading NW and NE between 1000 and 2000 feet. As noted on the sectional, flying through this airspace requires approval from the KMSY tower or approach controller(s).

It sounds like things worked out on your flight, but if you are ever unsure about something like this feel free to ask. We're a pretty accommodating bunch, and I for one would be more than happy to help explain things like this when needed

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C