Did you read their feature list? It clearly integrates with those services as part of their value proposition.
Honestly, I don't understand all of the API hate lately. People get upset when you don't have OAuth or integrate with their existing services, and then they get upset when you DO have it and it tries to integrate with your existing services.
For a community that is supposed to support each other trying to innovate and take risks, we've lately been really negative.
Authorize Teambox to use your account?
This application will be able to: Read Tweets from your timeline. See who you follow, and follow new people. Update your profile. Post Tweets for you.
And for google:
The site teambox.com is requesting access to your Google Account for the product(s) listed below.
Google Docs Google Calendar Google Contacts Gmail
wat?