Yes. Anything you write into your computer has the potential to be shared. The same way anything you write and send in the mail has the potential to be shared.
And yet, if GMail published email exchanges of a protected nature between someone and their lawyer, would you just throw up your hands and say, alas, digital communication is cursed?
Some digital activity should be considered private, and violating that privacy should have legal and social consequences.
Some digital activity should be considered private, and violating that privacy should have legal and social consequences.