If you can read emails sent to a given address, and send replies from that address, it basically is your email address for all practical purposes no matter who was meant to be using the account. This is not necessarily a good thing and better end-to-end security would be nice but it is what it is. Odds are the app itself would let anyone change the password and log in provided they can read the emails, unless it’s using some form of 2FA.
A smarter system won’t just take the mean of the votes from different instances but rather discard outliers as invalid input (flagging repeat offenders to be ignored in the future) and use the median or mode of the remainder. The results should also be quantitized to avoid leaking details about sources or internal algorithms; only the larger trends need to be reported.
Of course you could always just keep the collected data private and only provide it to customers willing to pay $$$ for access, which handily limits instance operators’ ability to reverse-engineer the source of the data. And nothing prevents you from using separate instances for public and private data sets.