Yes you are right-—In general Gibbon has done more damage to the accuracy of historical narration than not. He is the most well known of historians to allow his biases to take over when reporting historical events.
It was never a particularly strong case to begin with and I half suspect Gibbon of including it out of a bit of late 18th-century sensationalism. Nor did he claim it was the only cause of the fall of the Western empire. But I wouldn't dismiss it out of hand. The Church did abide, after all, and the (Western) Roman government did not.