I spent 3 years with a changing bag over the bar of my bugaboo cameleon! I didn't know that either, oops! But I used a Babymel one, they have a lot of choice and the bag lasted me over 3 years of every day use (it's actually still going but I would like to treat myself to a new one with baby number 2!) and it was also quite stylish and roomy.
Its up to you, but I would be very careful; the chameleon isn't designed to have a bag over the bars.
I guess the point I'm making is that bugaboo specifically say you shouldn't do it, and there doesn't seem to be any benefit for them to say this (it's not exactly a selling point). If they had said that you could only use bugaboo bags over the bars for example, then I would just chalk it up as a money-making scheme, but this isn't the case.
To be honest, this is one of the reasons I am so wary about buying second hand baby items i.e Ones that don't come with the original instructions and safety warnings. At the risk of being scare-mongery, did you read about the baby who died in a Bednest that her parents bought second hand? They didn't have the original instructions, used it in a manner not recommended by the manufacturer and the baby died.
Can't you just buy a bag that goes over your shoulder?
I have a bugaboo buffalo and it has clips to specifically hang a bag over the handles. It's also designed to take up to 10kg on the handles Maybe buy the velcro hooks that you can get everywhere and hook the bag onto that. They might advise against it in case the bag slips down and gets caught in the wheels. Or maybe they advise against it to stop the pram tipping if the the bag is too heavy?
I have a cameleon. Do not put a bag over the bars because you change the balance of weight with the carrycot and it may tip forwards. I did it once and realised quickly why you're not supposed to do it as I went up onto s kerb.
I keep a lightweight console on the bars for wallet, phone and keys etc. everything else goes in nappy bag in basket underneath. I have an oroton nappy bag which I love love love, but that's an Aussie brand that I'm not sure you can get in UK