I don‘t understand what you mean. Supervised learning is reinforcement learning, while not all reinforcement learning is supervised learning (e.g unsupervised learning is also reinforcement learning; i.e. reinforcement learning with unlabelled data).

Like you said, you can have reinforcement learning which doesn’t use training data. But that is not what my parent said. What they said is: since RL is used heavily in the training. And since reinforcement learning is a broad category which includes supervised learning, nothing in their logic disproves the strawman they created from an AI skeptic.