I think the link has one misleading statement and that is "If any part of Abe Lincoln's head is obscured by the tread, you're driving with the legal and SAFE amount of tread." (my emphasis)
As tires approach wear out, hydroplaning resistance and snow traction decrease rapidly. IMHO, it isn't SAFE (my emphasis, again) to wait until the point mentioned - you should remove the tires at 4/32nds of an inch tread remaining.
BTW the penny test yields 2/32nds of an inch tread remaining.
Also if ANY part of the tire is below 2/32nds (and this includes the shoulders of the tire), it is illegal to drive on in the US.
Hope this helps.