I believe it's listening based on an overwhelming amount of anecdotal evidence reported all over the Internet. (Where there's smoke, there's fire.) Including by intelligent, scientifically-minded people.
At the same time, it wouldn't take much at all for me to believe otherwise: a simple blinded test where some people leave their phones in a room, researchers come and talk about some subject (absent the owners), then leave without ever interacting with the owners of the phone.
There are two ways to do the next part: The owners of the phone 1 week later could be asked if they've seen any facebook ads on (topic). A control group would have to be compared (where researchers didn't speak on the topic.)
Alternatively, the subjects of the study could be given 5 random topics when commencing the study and asked to record any ads they've seen on any of the 5 topics. The researchers could then speak on 1 of the 5 topics (differing from person to person) and a statistical analysis could be performed.
A "proof" is a statistically valid correlation between what the researchers talked about out and what the blinded subjects reported seeing ads about.
A refutation is a lack of such a correlation. Easy, and it would convince me personally.
By the way based on the anecdotal evidence I strongly expect this study to conclude "facebook is listening."
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Note: there are a few loose ends to take care of. The researchers who are tasked with speaking on a subject are more likely to google it on their own phones. (Having been exposed to the topic), and those are in geographic vicinity. There are other similar possible mechanisms.
Perhaps the best approach is if subjects' phones are in a sound-proof vault and the researchers' speech is either fed into it via speaker/microphone, or not done so, but the researchers do not know for any specific phone whether it is able to hear them. (Making the study "double-blind", as neither the subjects nor the researchers know whether the subjects' phones have heard anything on a subject.).