Some streets change names as they meander along. Usually, this would occur at a cross street, but it could also happen at a municipal boundary or anywhere else I suppose. For example, there is a road called Lindbergh Blvd. that loops around St. Louis county and as it passes through the municipality of Kirkwood it becomes Kirkwood Road. Now in that case, there are plenty of cross streets along Kirkwood Road and probably cross streets at the two endpoints as Lindbergh becomes Kirkwood and then reverts to Lindbergh again. But what if Kirkwood was a sparsely populated town in the desert that is made up of a couple of houses and a gas station? It's possible that there might not be a cross-street along that stretch of the road even if you could get in your car and take it out of town and eventually reach a cross street somewhere outside the city limits.
It seems unlikely that your friend is right, but I think it's possible. Have you looked at any aerial/satelite photography?
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