Does Google track use of the Chromebook apps, etc, in any way? I would be concerned about privacy issues.
ALL app stores report some level of app usage to developers; amount varies.
Unless you choose to save a document off-line, nothing is retained on the machine.
From a patient/privacy perspective, using an encrypted connection addresses part of that.
If you don't want someone/proxy in the transmission, use a direct-connecting technology (e.g. RDC, 2X)
.... and this will *seem* obvious, DON'T SAVE YOUR PASSWORD in the app. Really.
