> Can [any storage that is not physically in my possession] be trusted with sensitive data?

No. You could make a case for E2E encrypted data where the storage provider does not have keys. That's pretty rare though. The point is, nobody gives a flip about your privacy. As soon as men with guns come asking for your data, any data business will hand it over without hesitation. Men with badges are only very slightly less threatening than men with guns, as everybody knows who the men with guns work for. So if you think anybody or any business is going to die on the hill of protecting your donkey porn collection, you're delusional.