Sorry techxan, I disagree. When listing into Google Local 7 pack (This is what the OP is talking about) Having a website is a MAJOR ranking factor. It didn't use to be so bad post pigeon update, earlier this year. Having a website is very crucial now.
Here is a fun post from moz.
http://moz.com/local-search-ranking-factors
Have you noticed what is actually going on since Pigeon? After piegon, a lot of maps listings have been eliminated, and the radius the maps are showing is a fraction of what they were.
Queries that used to throw a 7 or 10 box are throwing a 3 box, and those 3 results are super local to the search location. The reduction of the shown results radius is easily 1/4 to 1/2 of what it was before, which means there are fewer results, an they are close to the search location.
Now what I am seeing in my local searches is sites listed with google that do not have a website, but do have reviews and citations being shown in the maps box
if they are close to this search location.
I think if you search in a large metro area you will be able to duplicate what I am seeing. It seems to me tha the citations and reviews are carrying most of the weight, and in all almost all citations I have ever done the website of the business is optional.
The focus of the local algorithm has always been NAP, not NAPW.
Maybe in your area, the business that do not have a website simply do not establish a presence in local directories because they do not market online.
It will be interesting to see if anyone else has noticed this.
It would also explain what the OP is talking about.