No, it doesn't "depend on how you calculate statistics". Or rather you are not asking the right question. We do not care if a different person suffers a false negative. The question is if you, personally, are likely to suffer a false negative. In other words, will any given real world deployment of the solution be expected to suffer from an unacceptably high rate of false negatives?

Answering that requires figuring out two things. The sort of real world deployment you're designing for and what the acceptable false negative rate is. For an extremely conservative lower bound suppose 1 error per TiB per year and suppose 1000 TiB of storage. That gives a 99.99998% success rate for any given year. That translates to expecting 1 false negative every 4 million years.

I don't know about you but I certainly don't have anywhere near a petabyte of data, I don't suffer corruption at anywhere near a rate of 1 event per TiB per year, and I'm not in the business of archiving digital data on a geological timeframe.

32 bits is more than fit for purpose.