I'm not saying your neighbor is right, I agree she sounds either confused or just weird.
That being said, for the enlightenment of the members here, I have heard multiple cases of a single pseudostem flowering more than once, or continue growing leaves after it has flowered, though I've not yet had the chance to see one up close or throughout an entire plant cycle. I know this probably goes against everything you thought you knew about bananas, but given the right conditions, I don't think its impossible. As is the case with the 'Double Cavendish', 'Mahoi' (which is actually a different, possibly extinct cultivar, from the common one sold) and a few others, multiple meristems/shoots may be within a single pseudostem. The 'Double Cavendish' can branch off into these multiple shoots either on the inflorescence which is the common way, or it branch on the corm early on which makes a weird split/compound-pseudostem type situation (or it can do both, as seen below). In the second, rarer, situation, it is conceivable that you could have one shoot within the pseudostem produce fruit, harvest that fruit, and either have another shoot be pushing through the pseudostem and produce fruit later, or already have a visible second shoot which produces fruit later. There is also a lot of intermediary weirdness that can happen with up to 7 bunches formed in some manner (thats the most I've heard of, but I'm sure more is possible). However, you couldn't force a plant to do this, it would have to be a mutation that occurred to cause it.
Here is a normal type of 'Double Cavendish' dichotomous type action where the branching occurs on the inflorescence and comes out of a single normal pseudostem (photos found in our gallery).
Here however, is an example of a case where the split occurred much earlier and resulted in a compound pseudostem with two shoots, each bearing a branched inflorescence. In this case, you could really conceivably have a banana plant fruit twice from the same pseudostem.
These photos are details about the 'Double Cavendish' serve as a model of what can conceivably happen to any banana variety if the right mutations occur.