Scott - the answer is that depicts and depiction are inverse properties of each other, as you found out, it is defined like this in the FOAF spec:
<rdf:Property rdf:about="http://xmlns.com/foaf/0.1/depicts" rdfs:comment="A thing depicted in this representation.">
[...]
<owl:inverseOf rdf:resource="http://xmlns.com/foaf/0.1/depiction"/>
This means that if you have proper inference in your store, it doesn't matter which one you use, they should both appear.
FOAF uses a few things like that, primaryTopic/isTopicOf, topic/page, maker/made, etc.
FOAF also makes use of inverseFunctionalProperties, i.e. properties where a certain value is tied uniquely to a single person. The usual example is mbox, if you find two FOAF Person entities with the same email address, you can infer that they are actually the same person, since they are uniqiuely identified by their email address.