Seems a reasonable example.
I think you illustrated how Tom's "proportionality" can translate into a "regressive" tax rate, and along the way, by mentioning simplifying assumptions you had to make, you also illustrate how complicated it gets when you don't take into account all income and all taxes. That's the grey area where lobbyists try to rig the tax code to favor their clients, by exempting income and setting up a confusing tangle of different taxes computed on different bases.
Those definitions are simplified ideal cases, and you don't find those in the real world. Economics is really a dismal science.