[kps]

  > I have a hard time believing that. With a ton of stuff
  > all running inside of Chrome, it's much easier for them
  > to access each other's data than if they were standalone
  > apps.

Ah, the argument from incredulity.

If you're using X11, every command with access to the display server (which is usually everything you run) can read all keyboard and pointer input and screen output and inject arbitrary input.

[jlarocco]

And? That doesn't change by running inside of Chrome.

The only reason that's even a concern is because you can't trust Chrome Apps to not be malware.

On the other hand, when I "apt-get install <some app>" I know it's not listening to all X keystrokes unless that's a legitimate part of its functionality, because I trust the Debian team to only add trustworthy software to their repos.