No, there was no charge. Everyone we talked to at Tesla was very apologetic about the circumstances, and tried their best to get us back on the road. The main problem was that Goodland, KS, where we got stuck, is kind of in the middle of nowhere. Consequently, it took a while for a technician to get there.
I'm guessing this is what happened...I wasn't actually at the car when he showed up and was able to get it unstuck. The tips of the connecting pins on the car's charging port were broken off in the process of whatever he did. A mobile ranger replaced the charging port when we returned home (for which there was again no fee).
That's definitely possible. Although I think I see a missing bit of the outer shell near the shadow and the cracking is all on that side. My view was the repeated drops have weakened it, and with it attached to a cable, there's probably one side that takes more drop impacts than the other.