I have lived in various cities throughout the US, and I have never heard anyone use "paper bag" to refer to all types of bags when shopping. If I went to the supermarket and asked for a paper bag and were given a plastic bag (or vice versa), I would assume that the person was not paying attention to what I was saying.
This type of extension or generalization of the semantic domain is not unheard of, of course. For example, I can call any chalkboard a blackboard, regardless of its color.
However, I have seen no evidence of anything like this in regards to paper bags. It seems to me that this would be a difficult transition, as there is usually a need to distinguish between the two, and plastic bags are the more common option (i.e. if paper bags are available somewhere, then plastic bags are almost certain to be there too, but not the other way around).
Edit: It might also be worth adding that this could be a feature of the dialect of English in Kenya. Most Kenyans speak both English and Swahili, if not another local language. It is possible that the Swahili word for "paper bag" is also the general word for bag in Swahili, which caused this term to be used in their dialect of English as well. I am only speculating about this particular case, but this sort of thing certainly does happen in bilingual communities.