Firstly, I'm sorry to hear of your kidney disease and I wish you better health.
Secondly, many members here are (somewhat) aware of API keys and cookies and make decisions on an individual basis about how much trust they feel comfortable placing in a third party. I weigh such decisions carefully and I assume others do too.
As to authors not knowing how to use Amazon's own sales reporting, I think you give KDP publishers too little credit. I've never met anyone who didn't understand how to use the KDP sales reports - we simply find them clumsy and inconvenient, hence many seek more attractive options.
Regardless of the service and how it operates, it's certainly wise to consider whether a service is reputable, has a history in the business, and is frequently recommended by long time users. Even then, people and businesses that have been reliable for years may occasionally surprise you.
With all of that out of the way... I am a long time Book Report user and am (thus far) entirely comfortable with the service. I don't remember whether Liam has a history in publishing but I have no issues with a service provider coming from a publishing background, as many (maybe most) providers of author services do. If you are here for long, you'll find many members of this forum have varied skills and backgrounds in computer programming, art and design, and so on, and some hire their skills out to the community.
Book Report, by the way, is not free to users at my income level, so I'm not sure where the comments about them not being saints are coming from. Whoever imagined they were? They're providing a service for which I pay. If this sounds like a passionate defense of Book Report, it's not especially. I'm not guaranteeing this service in any way, simply saying I've been satisfied with my experience and, honestly, I can't fathom how they could operate in the way they do without a degree of data access. I can't comment on KDP Champ, because I've never heard of that one.
I'm not being rude. I give the benefit of the doubt that you are not running a competing service and you do not have a personal beef with the owners of the businesses you name. I imagine your warning is well intentioned and may be helpful to new publishers. Certainly it doesn't hurt to remind people to be wary, and any solid business can handle scrutiny and questions. Just maybe don't assume KDP authors are lacking in caution and so on. You're talking to people running small businesses, people who've been working in this industry every day for years. Doesn't mean we can't be scammed, but nobody likes to be assumed naive, regardless of to what degree they understand "fancy tech terms".
Also, the creators of some of these reporting tools are members here, so maybe they'll drop by soon to address your concerns. I suspect the eventual conclusion will be that some of your assessments are incorrect, some are accurate, and everyone must decide for themselves what they're comfortable with, as always.