Due to the nature of DNA your anonymity is directly reliant upon the anonymity of everybody you are related to, with a drop in accuracy proportional to the distance of the relationship.
Your DNA may be out there without any link to you. However if your brothers DNA is also out there but is however linked to him, then by comparison the fact that your DNA is a sibling of his, is easily determined. In fact this is the whole point of the current "Find you ancestors" craze.
The alternative to "they are lying" is "they are too incompetent to make the claim" and I'm honestly not sure which is more worrying. You can take your pick, they're both more or less equally terrifying.
I would think though, that the private corporation compared to a non-profit government agency is going to be faster at finding a solution given the same data. This will of course come with a $$$ cost.
Naively this sounds alright to me.
For me the issue is not that Y will be good, more that there are countless of potential research outside of Y that can’t be restricted and I wouldn’t agree with.
23andme for instance is not saying that their data will only be used for research that most people agree with. There is no “don’t be evil” mantra they harbor. And by definition there can’t be anything that 100% agree with and they can’t ask everyone for every use.
In that respect I think people should be able to contribute their data themselves to Y, without a man in the middle choosing where else the data should go. Short of that not contributing anything seems a sensible position.