The real value in the Apple ecosystem is the polished nature of OS X, which is light years ahead of Windows in terms of user experience, not necessarily the hardware that much anymore. But it does have the advantage that because they have control over the HW ecosystem, by and large things 'just work' and go on working. However, their software advantage which used to be substantial is not that great anymore and there are significant downsides too, newer Apple HW is notably less durable than it used to be, or so it seems to me. For that reason I stopped buying it quite some time ago. I can't afford planned obsolescence.
It would appear (from watching Rossman's videos over several years) that he would rather NOT buy parts with that fruit logo on them. Since the part is internal to the customer's gadget, the customer wouldn't know (or care) whether it was a "genuine" part or not. Rossman is not in the business of making Apple look good by repairing their lousy products. Or by claiming that he is using "genuine" parts (whatever that means). Rossman is in the business of fixing his customers products so that they can get on with their lives without going to the Idiot Bar and losing all their data. Or being told that their gadget can't be fixed because there is a newer model available for purchase.
The problem, of course, is when ordering from your average Asian source, you really never know what you are buying. They may claim that what you are buying has (or has not) any sort of logo, and is (or is not) a "direct replacement". But you are left at the mercy of the vendor whether their claims are accurate or not. And, then when the unknown goods arrive at the US port of entry, if Apple has their way, the goods will be seized as "counterfeit" whether they are or not. Because they have the $$ to buy the best lawyers on the planet to do whatever they want.
If a part is a non-Apple part and is honestly represented as such, or a refurbished genuine part, and represented as such, either way, I don't think Apple should have any right to control any aspect of the transaction. To give them that right would upend the rights that come with ownership of products of every kind in a really horrible way. That would be a real problem for people because suddenly, companies of all kinds would start trying to do the same thing with everything people buy. They already are trying to pull tricks like that at every opportunity.
Ironically, it would become a "situation" that could turn around and bite Apple's reputation hard, exactly what they likely would be claiming they were trying to protect.
Also at the same time it would make people more everywhere aware of this important consumer rights issue, the
right to repair.
The only thing that I think they could possibly hold against vendors and win is if a vendor sold used Apple parts - representing them as new.
Customers have the right to know if a part is refurbished to original factory specs, or used/as-is.