I know this is an old article; however, I came across this and wanted to add something. While it may seem illogical or that there isn't a right or wrong answer, you must remember the focus is to make the document grammatically correct. Your question can best be answered by revisiting the basic definition of a proper noun. While we would say "figure(s)" is a common noun, you are speaking of "Figure 3". Since this is a single occurrence, it would be considered a proper noun.
Another example would be to think of how proper nouns are applied to seasons of the year. If you are speaking of the season generally, you would say something like the following.
I enjoy going to the beach during the summer.
However, you may want to talk about a specific season that had an event worth noting. In this case, there would be only one and it would be used as a proper noun.
During the Winter of 1988, we had a horrible snow storm that caused the entire city to lose power for an entire month.
I hope this provide clarity for those seeking the correct usage, as there is a right or wrong answer here.