The song doesn't mention the circumstances, but there are a lot of situations where this isn't reckless driving, such as:

• winding roads, like in the mountains - visibility is reduced and stopping distance is lengthened
• rainy conditions - stopping and steering are significantly impacted
• distracted by your date - reduces reaction time

It's quite understandable for a young driver to not properly compensate for the above. The fact that the girl asks the driver to hold her tells me that this likely wasn't reckless driving. Here's the origin of the song:

Cochran said he first had the idea for "Last Kiss" when he was living in Thomaston, Ga., near a treacherous stretch of two-lane rural highway. "There were two or three accidents a year there and people were always getting killed," he said. "It was horrible. ... So I said, 'I'm gonna write a song about a car wreck.' "

It could probably have been avoided, but that doesn't mean the driver was reckless. It seems the infrastructure was likely the main culprit here.