Do I need to trust Telegram for this to be secure?

Security Official telegram.org Source

When it comes tosecret chats, you don't — just make sure that the visualized key of your secret chat matches the one in your friend's secret chat settings.More about this below.

Official Telegram Reference: https://telegram.org/faq

Part of the TGWAY.com Official Telegram Knowledge Base (98 Verified Q&As).