Verdict: Almost true. 

According to Spencer and eye-witness Gary Rand, at the 1978 Loudon National, on the final lap of the 250 novice race an unleashed dog crawled under the fence by the side of the track and wandered onto the racing surface. 

Spencer continues the story, "I didn't realize until it was too late that the dog was directly in my path. I remember that it was a big dog, as big as I was it seemed. I hit it-hard-and the collision bent the shifter. I had to finish the race in fourth gear." 

Rand was standing track side and said the incident looked terrifying from his angle, and he was surprised Spencer didn't crash. "Since that day I've always wondered why people bring dogs to the racetrack," he said. 

And, as for the part of the tale where the dog was eviscerated by the collision, Spencer and Rand both say that post-contact the dog crawled back under the fence and wandered off.

Ends

Related:
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