> Leading zeros don't do what you think they do
It's has been pretty normal for clocks with digital displays to include leading zeros for seconds, minutes, hours and/or days for about a century. Doing the same for years, while unusual, doesn't seem particularly confusing. And of course, there is precedent with things like ISO86011 - where 0400 is the year 400 CE.
I'm not sure why one would assume it was a truncation of 101931. That doesn't really make much sense. The first decamillennium digit started at 0, just like the first millennium digit started at 0. 101931 would be 99,905 years in the future.
> how people say 03 when they mean 2003
Making people think beyond that form of casual shorthand (even omitting the apostrophe which would indicate the omission!) is sort of the point? Never mind that 03 doesn't necessarily mean 2003.