Their board and staff consist of 27 people, including all directors. The breakdown of their expenditures structure is on the right sidebar of the donation page:
5% Fundraising
11% Administration
84% Programs and Services
At the bottom of the same sidebar are links to their past financial documents, up to 2010 ( http://www.freetheslaves.net/Document.Doc?id=251 ). In that are their compensations per-employee on page 7 and 8. Of the 12 employees listed, no one received compensation of more than $36,000, and the total compensation for all of them was less than $80,000. Most received zero compensation. The average hours each work per week are also listed, so one can take an educated guess about the corporate structure.
Their total revenue (~$2.9 mil) and expenditure (~$3.1 mil) are listed on page 12. For that year, they operated at a ~$200k loss, leaving them with ~$1.1 mil in assets at the end of the fiscal year. More itemized details are available within.
I think it's good to be skeptical of charitable organizations given the corruption that has been exposed in some non profits. As to why 2010 is the last available? The 2011 returns were due in April 2012. Perhaps they're waiting on approval from the IRS before publishing it. Someone else could chime in here with a better reason.
As for the "don't spend money on <x> until <y> is resolved" mentality...I see it all the time:
"It's such a shame that people spend money on Instagram/Facebook/Twitter when space travel/clean energy/cancer research/etc is such a greater cause..."
The communist anti-capitalism rhetoric of the mid 1900s was similar: comparing the luxuries of the rich against the suffering of the lowest common denominator. Perhaps there was a similar pitch on the capitalist side against communism--I just don't see it.
I think the beauty of this organization (and most non-profits) is that it's based on voluntary participation. They're not forcing anyone to donate. Their emotional manipulation is on par with the typical commercial for weight loss, beer, cologne, anti-depressant medication, etc...and in my opinion, their cause is more noble.