Nope... What you're talking about is not privacy sensitivity, but trust.

For you, you don't trust the provider of the software, so you mean being able to put a barrier around your life, and the delivered software... you think that by running in a browser, you're preventing that code from being connected to anything else... However, anything that happens in that code is directly connected to the provider, whom you don't trust.

I'm referring to the opposite... having something connected to your life, but having a barrier disconnecting it from the outside world... It involves trusting the provider of the software (maybe it's open source), but even if you don't, you can install an app, cut the network, use it locally, then delete it before restoring the network, and you have a guarantee that what you did with it was private... It's possible to build that into a web app, but most websites don't work offline, where most apps (though not all), do work offline... even if it requires an initial network session to establish authorization