You have a user who has not been trained to not install random software, is fooled by extremely common ads, and who does not have the basic judgement necessary to not flail about when presented with something they don't understand but to consult someone who will understand.
This is a recipe for the exact scenario you described, but is in no way dependent on Firefox's Java messages. Any message appearing on their screen that they don't understand can be the trigger, including scammy ads encountered by millions of people in routine daily browsing.
[1] https://dl.dropboxusercontent.com/u/1643240/outdated_java.pn...
[3] 1 & 2 taken from this thread: https://news.ycombinator.com/item?id=6590877