I have many 0.01 keywords. Working on content network. There is two ways to initiate them: 1-CTR is great and if you bid 0.03 adwords will probably lower them by itself to 0.01. Quality score must be "Great". 2-Force 0.01 by manually entering that price.
Have MANY 1 cent minimum bids on the search network. Doesn't mean 1 cent is all I'll be paying though. Many of the 1 cent minimum keywords I end up paying $2 for anyway because of the market competition.
Yep, lots have a min bid of $0.01 but that doesn't mean you can bid that and actually have your ad show...