Sci.. why are you repeating yourself so often? As I said in my last post, there's really no way to know for sure given the available information. You have your opinion, I have mine, others have theirs. No reason to ram it down anyone's throats.
"President" is just a word in the end. Every country with a president doesn't have that individual serve effectively in the same role. Different governments, cultures and languages have differing meanings for the word. This becomes even more pertinent when you bring other alien races into the equation.
I honestly don't think a planetary alliance is going to elect it's head of state based on popular vote or even in an electoral college fashion. This would effectively lead to one species dominating the position, probably humans. The simplest solution -would- be for the council to elect the said leader, since you're touting that the simplest approach.
If he's called president instead of prime minister, chancellor or grand panjandrum, so what? It's a word and the meaning of it is only applicable to the place and time of the Federation and her member races in the 23rd/4th century in this case.
But in the end, yes we can argue each other in a circle on this one. There's not much evidence either way. Even the guy claiming the Federation is a military dictatorship could make a convincing case with the available information. I'd think he's wrong, but hey I can't -prove- it, since it's a fictional setting that hasn't revealed that said information.