Perhaps a better example would be the kilo. Officially a kilo is a kilogram, but in common everyday use we call it just a kilo. But a 1000th of a kilo is not a microkilo but a gram (you drop the kilo from the kilogram and you're left with gram).
You appear to be mis-understanding the metric system (which, incidentally is what prompted that original reddit poster to propose "bit").
The way the metric system works, values are expressed in the following format:
Using the same prefix or multiple prefixes is formally not allowed: since it would obviously lead to confusion. (sometimes is happens with really common prefixes though. The SI system formally defines its base-unit for mass as the kilogram)
In the kilogram example, the kilo (meaning x103) is actually the prefix. The "gram" is actually the base-unit. Thus it does not make sense to say 1/1000th of a kilo.
Common prefixes:
- Mega M(x106)
- kilo k(x103)
- (none) (x100)
- milli m(x10-3)
- micro µ(x10-6)
Incidentally, the proposed "mike" short-hand for 100 satoshies does the same thing: (mostly) keep the prefix, but drop the unit (which is implied by context).
