dear JAN
I imagine many airports with a field elevation of 4000' msl would have a pattern altitude of 5000' msl.
Maybe you live somewhere near sea level. There is a field near one place I live that you would be 900' below the ground at 5000' msl.
So, No reason to doubt this story . He is just flying somewhere high, like the western United States. Try it. You'll like it. There are airfields in the USA that are above 8000' in some places and you have to get special data to fly there from the manufacturer of some planes.
I think Mexico city is at or near 8000'.
I'm sure you get the idea.
JAN, where do you live?