A poet may memorise verses or comment insightfully on other writers without necessarily being able to improvise with ease. Producing a coherent new answer on the spot requires a different kind of command.
The stranger matches the imagery of a difficult verse almost immediately. Within the story, this demonstrates vocabulary, imagination, judgement and poetic fluency. It is a practical display of skill, though such a performance should not be confused with independent documentary proof of every authorship claim he has made.