That text, bookworm, appears to say that any State you overfly is entitled to force you down for an examination, which is obviously true. And that one has to do this at a Customs airport, which is also obviously true.
I was talking of a voluntary refuel stop. A Customs airport has an "airside" (at least, during its Customs hours) which means one can land there without leaving "airside".
How do airlines and business jets do their refuelling, without everybody (or anybody) having to clear Customs?