Again, the problem is that the team at 37 Signals invested time and money into developing Basecamp. It’s not like they open sourced their code; someone came along and ripped off their UI. 37 Signals is a for-profit company, and those profits depend on people subscribing to their services. By offering similar functionality based on their research and development for free (and luring users like @jmstudio above), you are in fact stealing from them—not just IP, but actual revenue as well.
If you want to stand on the shoulders of someone and build something greater, that’s fine, but only if they consent to their work being used in that manner. AFAIK, 37 Signals has not given this consent with regard to Basecamp.