Gosh I wonder where I get this impression from.
You conflate 'leadership' in the sense of providing inspiration or tactical coordination, with Leader in the sense of an officer, Noble, or other position of legitimate authority. It's an easy mistake to make, since officers and nobles who were particularly good at their job evinced both sorts.
And, you found no support for your idea that the player was in any way supposed to be bossing around other players, quite the contrary, those are support abilities, the power of which flows to the ally. The player who's character is returned to the fight by a Warlord's inspiration has more opportunity to make decisions for his character, not fewer, for instance.
But I'll keep an eye out on those pages, for when you post and ask them to stop spreading false stereotypes.
Provide links to any such you find here on ENWorld, and I'd be happy to do so.
My thing is that I really don't like being told what my character thinks. And so many things about the Warlord...again, the versions I see today, not whatever was in some book 15 years ago...
10 years ago, but out of print is out of print.
simply scream "your character admires/obeys this other person's character." So in my mind that is you dictating to me how to play. My only option is to mentally re-fluff it into magic...
Well, not, your /only/ other option (not even a good option: if you were to "re-fluff" it mentally as 'oh, this must be magic' then it would fall apart if it ever happened in an anti-magic field, at best you'd be RPing as delusional - magic or not has mechanical implications, it can't just be fluffed away).
More viable options might be: consider what your character would or could or might think, that would be compatible with getting the benefits, and appropriate to the relationship the two PCs have. You may be inspired by someone you look up to, for instance, but you may also be inspired to protect someone weaker than you, or to out-perform a rival, for other instances.
And, if you just absolutely cannot come up with any rationale, then, like a Paladin refusing healing from the ally-of-necessity Cleric of Asmodeus, or the old-school Barbarian refusing* the magic-user's Haste spell, you just turn down the benefit.
It's a valid RP choice.
It might get you & even the whole party killed, but, hey, some heroes have tragic flaws.
Also, basic character-concept compatibility like that is something that, if it's a potential issue for you, really needs to get hashed out at some point, preferably a "Session 0," but before it gets to be an issue, at any rate. One player may not feel that a Warlock is a suitable ally for a Divine character, for instance, and that could be hammered out one way or another - the characters could 'not get along' RP-wise, but still help eachother when the chips are down, for instance, or one player might just choose a different character on the grounds of irreconcilable differences - but, hey, at least they each had a /chance/ to play the characters they wanted to.
* technically you couldn't refuse a spell in that sense, but maybe the DM would let you save vs it.