How can you be sure?
Firstly, the poem refers to Pensher Hill, secondly, Penshaw hill is a "ring" hill, it has several lines of earthworks which probably originally went all the way round. I have come accross a couple of worm myths which seem to be inspired by a tinged hill.
I'm aware that there are definately strong feelings for both opinions but I have yet to see any documentory evidence (other than the name) that links worm hill to the Lambton Worm story.
Worm Hill is also an ancient earthwork by the look of it, and it may be that the confusion is because the 19th century interpretations condensed an earlier tale which perhaps included both hills.
What is the oldest reference to the Lambton Worm? To be honest all I've seen is the song.
I can say, I too am local, and our history teacher, who was also a leading member of the local history society clearly linked Penshaw Hill with the Lampton Worm, as does most literature currently available (not that that's anything to go by of course).
To my mind, both hills are important, and were key features of the prehistoric landscape in that area.