Neither of those instructions were given. The controller said 'we're gonna' have to ask you to circumnavigate at this time' and there indeed was a question as to what that meant.
And? Don't forget the rest: The pilot acknowledged that instruction (which normally means the pilot fully understood it), gave his plan, and the controller then replied, "As long as you go around
our airspace, that'll be fine." When the pilot came back with a "You mean I can't even come into your class C?" the controller countered, "Circumnavigate around Lake Jessup and east of the river, will be fine, at or below 500 feet."
Now, could the controller have been more clear had he used better phraseology, as in "Remain clear of class C?" Sure, but there was no evidence in the clip that your pilot buddy was confused about what the controller needed, and the excess banter between the two of them presented a clear picture (at least to this low-time 1,200 hr pilot) of the requirement.
Furthermore, upon listening to this another time, it is apparent to me that your buddy was attempting to cut the corner back to the north well early of where the controller wanted him, as evidenced by the continual request by the controller to push him further east. In looking at the sectional chart, you will see that all but the eastern-most sliver of the lake is inside the class C inner ring and your buddy kept stating that he was over the water, which implies that he was well inside class C even though the controller stated, "as long as you go around
our airspace, you'll be fine."
I think my first assesment was correct. You guys are getting all wound up over nothing.
And you are attempting to spin this incident in favor of your friend when clearly mistakes were made by him. In the end, what was he trying to protect? A $2.50 fuel savings? Please.