While your thinking here makes sense, it is better to honor truly Free as in freedom / Libre / Open Source software instead of funding proprietary software. FLOSS is also made by hard-working people and given away mostly and used by people who make money. But if you support FLOSS, your support goes to help everyone in the world, whereas if you fund proprietary software, you help advance something still under exclusive control by the company and not respecting everyone's freedoms.
It would be better if trello had servers I could download, but they don't. I like their system, but I don't trust them with life details like bank account numbers and such. (though trello really isn't for that, see last paragraph)
That said, being the heavy FLOSS zealot that I am, I don't have a problem with what trello is doing, per say. They're offering a service, and paying for a service is fine. Particularly a well executed service with good support.
The service they offer isn't just access to an application, though it's a shame they keep that application to themselves, they offer a hosted server and storage for everyone to access. There's nothing morally wrong with it.