Well it's an odd historical fact that he's quoted anyway. It can only be verified if all clubs kept records of their use of ball boys, starting with the very first time. I suppose you have to start with, "what does he mean by ball boys?". Do they have to have been paid to be counted as official? Or do they have to have been appointed by the club to do the job of retrieving the ball, even if they weren't being paid? Or does it have to be their only job during the game (rather than other staff doubling up)?
Being paid makes it easier, because clubs keep accounts. But if not, then it comes down to the efficiency and bureaucracy of the club.
At United, as you say, there will have been an inbuilt need for ball retrieval. They wouldn't have wanted spectators racing each other onto the cricket pitch as soon as a ball went a bit wayward, so either they left it to the players to run the length of the field to fetch their own ball - hard to imagine - or there was a system (however basic) in place.
The problem is, I can't see anyone recording it in an official document. So, a bit like the oldest football ground argument, it comes down to the first recorded use, which is quite possible and what he should have said.