I did in fact wrap the reading code within a
if (Serial.available()) {
..
}
I removed it just before posting to check if there were ever no bytes available, and there aren't.
I get a small set of unique numbers, which are (hexadecimal, in descending order of occurrence): 84, 27, BC, 21, 37, 31. Different buttons give different numbers, but I find it hard to find a pattern in the order in which these numbers occur. But the real problem I wanted to ask help with here is this: when I write out these numbers again, the pattern I see in the Serial Monitor does not vaguely resemble the direct output from the wireless receiver. So apparently I make a conversion error somewhere with the bytes read. I expected that a Serial.write() of the bytes that an earlier Serial.read() gave me would give the same pattern.