I don't think you can use any of basecamp features for free. [1]

They make money, that is not up for debate.

(and yes, I know, their platform, their rules, etc etc, but nothing about that says people cannot fight it, and make it politically difficult to let them bleed money from people for a very basic service.)

1 - I have never used basecamp, or looked into it, so YMMV

You can use any app that integrates with Basecamp without paying a cent to Basecamp for the integration itself. You can even browse a list of integrations hosted by Basecamp. https://basecamp.com/extras

Basecamp isn't free, but neither is an actual IPhone. In the case of the tools that are enabled on their platform, Basecamp's library doesn't require paying basecamp, and Apple's does.

And neither is my computer or internet connection. But that doesn’t mean I expect BaseCamp to be free. Can I distribute my games on any of the console manufacturers system for free?

And before someone responds that you can buy physical games for consoles, they still have to pay the console manufacturer for each physical game sold and the console manufacturers have to approve it.

Can I use BaseCamp’s APIs for free and create my own app? In fact, BaseCamp just announced that they will not allow third parties to integrate with their software that use their platform to track employees.