Can you explain what the intent of Bitbills is with this? It seemed from things I have read so far you would like anyone that creates a cold wallet product or service should have to license this technology from Bitbills, which is horse crap frankly.
Assuming this is not their intent then I would guess the problem is that they feel they "need lawyers" (something it seems is in the blood of most USA citizens) who will advise you only in the way that they think they will be able to make the maximum amount of fees from court cases (so the more court cases the better in the mind of a lawyer - thus the advice to make the patent as wide reaching as possible).
This is probably not so much their own fault as the fault of a broken system that pretty much lets anyone patent anything and then lets the lawyers make the money in fighting over whether the patent is actually sensible or just plain rubbish (an exercise that only enriches lawyers).