Should a restaurant be required to give an ingredient list when asked?

Here’s a little backstory:

This is about a steakhouse in my town that is a single restaurant, not a chain, and family owned & operated. My husband and I went last week and sat at the bar. The woman next to us was fixing to order, when she informed the bartender that she had allergies/intolerances to sardines (commonly found in Worcestershire sauce) and barley/gluten. She asked if the marinade contained those ingredients, and if so she’d just leave the marinade off. The bartender didn’t know, so the owner came up to answer her question. He told her that because it was a “secret family recipe” he couldn’t share the ingredients with her, and told her she’d just need to leave the marinade off as he couldn’t disclose the ingredients. She ended up paying for her drink and walking out. This got me thinking, should a restaurant be required to give out ingredients? Should a secret recipe protected even if you’re serving this dish at a public restaurant?