Commercial? In what manner? It's not a commercial enterprise in any way, and how's it falsely trading. The only thing we're trading is the love for these brave vets. Are you trying to rain on our parade of gratitude? Hell, I even link to their site off the logo. Any cease and desist request from the Swifties would be happily met with immediate compliance. Are you suggesting I cease and desist? If so, on what authority?
You don't put some other guy's logo on your web site. Never mind the legalities, it's wrong. Unless you are formally connected in some way with SwiftVets and POWs for Truth, you should not be branding your web site with their logo.