Byzantine

My friend Robby gave me the book Truman on audio before I left the US. Now that I finally have IPhone I was able to listen to while during commutes. There's one line I simply didn't understand. In the run-up to the 1944 Democratic convention there was a movement to dump Vice President (and Iowa boy) Henry Wallace. Of the names being considered Truman made it clear he didn't want the position and Roosevelt gave no indication where he was leaning... and kept putting off any comment.

Author David McCullough wrote that Roosevelt chose Truman in a "Byzantine manner." Huh?

The closest definition I could find is this:

"...characterized by elaborate scheming and intrigue, esp. for gaining political power or favor..."

That still doesn't really tell me what byzantine means. Is it good, bad, or just very political? Roosevelt was president so it wasn't him seeking power and McCullough argues that nobody wanted the Vice Presidency less than Truman. Please give me your interpretation.