Anyone who has used Telegram for more than 5 minutes knows there are secret chats. The effort being made to rig the information against Telegram also tells a lot about its relevance.
The telegram desktop main developer said[4]: "Well, I'm afraid there isn't. They are just not in high priority, many other important things first."
It seems stickers, funny bots and GIFs have more priority over security. I think this tells a lot.
[1]: https://github.com/telegramdesktop/tdesktop/issues/871
[2]: https://github.com/zhukov/webogram/issues/126
[3]: https://github.com/vysheng/tg/issues/1189
[4]: https://www.reddit.com/r/Telegram/comments/2z24ly/how_to_sta...
Secret chats are not enabled by default, and most users don't enable them; so yes, messages are generally stored without encryption on the Telegram servers. That's a more neutral way of presenting the information.