What launches an ancient "Update Helper" and how do I confirm it's not a trojan?
As others have mentioned, this discussion has some good tips for accomplishing this.

I have not tested any of these solutions as I still frequently use Google Chrome and do not want to delete these files myself.

If your Library contains a install.py file:

python
~/Library/Google/GoogleSoftwareUpdate/GoogleSoftwareUpdate.bundle/Contents/Resources/GoogleSoftwareUpdateAgent.app/Contents/Resources/install.py --uninstall

or:

python
/Library/Google/GoogleSoftwareUpdate/GoogleSoftwareUpdate.bundle/Contents/Resources/GoogleSoftwareUpdateAgent.app/Contents/Resources/install.py --uninstall

If your Library instead contains a ksinstall file:

~/Library/Google/GoogleSoftwareUpdate/Google‌​SoftwareUpdate.bundl‌​e/Contents/R‌​esources/GoogleS‌​oftwareUpdateAgent.a‌​pp/Contents/‌​Resources/ksinst‌​all --uninstall

or:

/Library/Google/GoogleSoftwareUpdate/Google‌​SoftwareUpdate.bundl‌​e/Contents/R‌​esources/GoogleS‌​oftwareUpdateAgent.a‌​pp/Contents/‌​Resources/ksinst‌​all --uninstall

Test if it worked by running defaults read com.google.Keystone.Agent. If it worked you should see Domain com.google.Keystone.Agent does not exist.

Alternatively you can also disable the updater without removing it completely by running:

defaults write com.google.Keystone.Agent checkInterval 0. The 0 essentially tells the updater to never check for updates.