They were a success long before Ruby on Rails. The article doesn't quite connect the dots, but they were so successful as a consulting company that they created Basecamp as an internal tool to manage their own products. And then Basecamp was such a hit with their clients that they sold it as a service. And when that service became a massive success, they open-sourced the framework they'd built it on. [1]

[1] https://basecamp.com/about/story