It's a curious fact that rulebooks more often seem to spell out you can't make non-integer bids than say you can't make uncovered ones.
In the case of AR, the rules state that the winner "takes the share and pays his final bid to the treasury of the company that sold the share."
Rulebooks only need to specify what may be done. They do not need to specify what many not be done. Since it does not specify that you can at any time pay less than your final bid, it seems reasonable to me to conclude that you cannot bid less than you can pay. I'll keep your observation in mind though when I write rulebooks in the future.