This sucks Jo. Honestly, I would have told them no and then insisted that they take me to the nearest police station first. I don't know if you have read one of my posts that outlines these situations. https://medium.com/digital-global-traveler/what-to-do-when-a-stranger-asks-to-see-your-passport-in-a-foreign-country-e7aaea51f858

But I understand the need to prove your innocence when you are simply a visitor to a country. Mexican police are certainly famous for their corruption. It's very sad.