Sadly thats simply not true, they do not have to prove anything. Show me how you would handle it and why its extremely unlikely?
If they suspect it, they can do what they like, there are countless examples of this actually happening. Your only recourse would be legal action and its quite unlikely you'd be successful, aside from the costs of doing so.
This game that some of you seem to wish to play with trying to deceive the manufacturer is all well and good, i say go for it if you can afford the risk.
Add in that most people purchase their cars on finance and you're in an even worse position.
Youtuber LLF aka riccardo senior found this out to his cost last year.
Car manufacturers have to obey contract law, just like the rest of us. They have agreed to provide you a warranty and can't revoke that agreement without a valid reason. Is a tuning box being fitted a valid reason - yes! Of course it is, but if you remove the box and wiring loom every time the cars goes back to the dealer then how would they know. I'm sure you don't dispute that there would be no physical evidence left behind. Nor any changes to flash counters or checksums within the ECU itself.
Perhaps they rely on the ECU having gathered sensor data? The problem is that using historic data alone would make it very hard to pinpoint the cause of an issue. Not to mention that well designed tuning boxes intentionally avoid messing with sensor data for things which are logged for long periods of time. An example would be avoiding the fuel pressure sensor because most ECUs log long term fuel trims.
But what if the ECU is able to outright monitor for tuning boxes? Well, you'd be screwed, but I can't find any evidence of this technology being in play. You earlier posted a link which mentioned the TB1 code used by VW to mark cars which were suspected of having tuning boxes fitted past or present. However I've been unable to find any examples of people's warranty being voided based on this code. I also can't find any reliable info on if the code even exists. It seems to appear on one screenshot of a TSB from VW however no other examples of it appear online anywhere.
This seems suspect when you look at other such codes. The TD1 code for example which concerns remaps, has multiple documented cases of people's claims being denied based on it along with being mentioned on multiple internal VW documents.
You're right regarding mods to financed car but what happened to Ricky isn't really relevant here. His mods were far more extreme than a simple tuning box and widely publicized.