In terms of trust, this isn't any different from having to trust that your web service provider will protect your data. Granted, there is a substantial difference in choice - you likely only have one option for electrical service to a home, but a plethora of web hosting choices. Thus, this is fundamentally a regulatory issue (ie. call the Corporation Commission).
The alternative is to do it yourself (run your own server, make your own electricity with solar/wind/etc.), which, if you're really concerned about this, you might feel it's worth doing.