By the rules, I can't recall anything that says out loud that you are supposed to roll a bluff check in that event, so (unless disproven, because proving negatives is impossible unless I read all the D&D 3.x material again) I'd say this is a case of the DM using his authority to ask for a roll.
Now, was what he asked fair?
Of course this is deep into the speculation zone, but I think it has a solid basis.
Since the rules tell nothing about rolling to disbelieve true things, your DM could have just said, "No, the NPC does not believe that you're telling the truth. In fact, he believes you're either lying in a very convincing way or you've been fooled into believing by someone else."
Diplomacy, bluff or charisma checks of any sort are useless to convince him you've not been fooled, unless you're known for not being gullible (and in that case, they're an automatic success).
Bluff is not really great even for convincing someone you're not lying: I would have asked for a diplomacy check instead. Truth is, bluff is often used to represent body language (I think it was used to relay messages to people not speaking your language, but that might just be my DM's ruling), so I see your DM's reasoning.
Were you better at diplomacy than bluff, I'd see a problem in your game. If not, he just gave you a (small) chance to luckily shine.
Players Do Not Initiate Passive Checks
The operative word is passive. If a player is actively searching/examining/studying/watching, it's active, not passive. If a PC is actively using a skill, they roll for it instead of the DM using a secret passive check.
The only exception to that rule is the one you quoted: the DM can use a passive check to find the average result of doing the same thing over and over again, regardless of whether it's active or not.
In general, the point of the existence of the passive check is so that the DM can determine something when the players aren't expecting to notice anything. In those cases asking them to roll would give away that there is something, so instead D&D 5e provides DMs the passive check to avoid giving away the secret. When to use passive checks is much easier to grasp when you look at them from the perspective of the problem they were designed to solve.
Also as a consequence, PCs are rarely in situations where it makes sense for players to ask for passive checks — after all you can't know to check what you don't know is there to check! This puts the responsibility for ensuring passive checks are made when they should be on the DM's shoulders. As a useful aide for this, it helps for the DM to keep a note listing each PC's name and their most important passive checks. Just having the note can be a small spur to remind the DM that passive checks should be kept in mind during interactions with hidden things, NPCs, motives, and etc.
To answer the titular question, this means that a player never states that they're making a passive check. It's something the DM does as the situation requires.
Best Answer
It can be any of the following approaches:
The rules support all but the last of these as viable skill uses.
A lot depends on the GM, but as much on the players. If you're constantly being denied skill uses, ask the GM privately if he's not seeing your hooks for skill challenges, or if he's just not interested in that style of play. It might be either, or neither.