It definately isn't base 27, or you would need to use **27 not **26.
It is base-26 in the same way as feet are in inches base 12, or hours are in minutes base 60. The only unusual thing, in computer terms, is that it is a 1-based number system not a 0-based, but in the real world, most things are 1-based.
We measure the months 1 - 12 not 0 - 11, the metres in a kilometer, millimetres in a metre, grams in a kilo etc etc. as 1 - 1000 not 0 - 999
Update:To reenforce this point. If the system where base-27, then the cycle would repeat every 27 symbol. It doesn't it repeats every 26th. vis. It MUST be base-26.
If it makes people more comfortable to think of it as A representing 0 and Z representing 25, so be it, but for it to be base 27, you would require 27 symbols, but there only 26.
"When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." -Richard Buckminster Fuller