This is just a cover story. The real reason why buses arrive in threes is that they set off, from the bus station, in threes. There's little attempt to conceal it. A bus conductor nips out of the garage, looks shiftily left and right, and then shouts back 'Bob! Fred! Jimmy! Go! GO ! GO!'
Three double deckers then steam out, racing towards their destination in a competition to see who can arrive first and with least passengers.