I think the conclusion is the Honda DI engine has two sets fuel injectors, the primary system (DI) injects fuel into the cylinder and not through the inlet valve port, the secondary injection system is to the inlet port, the purpose is to spraywash and clean the inlet valve port of carbon build up.
Carbon build up, cheap fuel is to avoided!
Many years ago at a classic car show, I had a conversation with an owner of an old post war Morris, he had rebuild his engine only to have to decoke severe carbon build up within a year of regular driving, he blamed the carbon to discount grade supermarket fuel. He said no problems with premium fuel such as Texaco premium fuels.
Diesels cars, my brother had an Vauxhall Astra diesel, on supermarket discount fuel the vehicle struggled to pass the MoT smoke test, if he used the vehicle on premium diesel fuel for several tanks before the MoT , the vehicle flew through the smoke test, I wish I had the Mot test printouts to give figures to my post.
Moral, you get what you pay for, cheap fuel is actually the expensive option, it causes problems