Bonus feats which don't require prereqs will always explicitly state that that's the case. Easiest example is the Master of Many Styles Monk and the bonus style feats they get.
Edit: Fighters would be absurdly strong if they got feats without needed prereqs every other level. Improved Critical and Vital Strike with a rapier at level 2? Don't mind if I do!
If you have to select the feat from a list (and it doesn't say you get to ignore prerequisites), you need to meet prerequisites.
If you are being given the feat forcefully, you do not need to meet prerequisites.
The Gendarme is weird, however, in having Spring Attack in its list of feats (especially with how ineffectual it is for mounted combat). Since you need to meet the prerequisites, but there are no clauses for what happens if the only feats left to select are ones you don't meet the prerequisites of...
Some bonus feats ignore prerequisites. These have text like:
He can choose feats from his selected combat style, even if he does not have the normal prerequisites.
A monk need not have any of the prerequisites normally required for these feats to select them.
If something gives a bonus feat, but does not explicitly specify that you do not need prerequisites, it's a fair assumption that you do. I mean, otherwise classes that get bonus feats from a large set (e.g. "Combat feats" or "metamagic feats") would be completely unreasonable.
If a class/archetype grants a specific feat (example: the BARD archetype Dawnflower Dervish grants the Dervish Dance feat) and does not mention prerequisites, the assumption is that the granted feat functions even if those prerequisites are not met.
If a class/archetype grants a SELECTION of feats (either from a given list or from a specific type of feat such as Metamagic) and does not mention prerequisites, the assumption is that the feat can be selected but will not function if the prerequisites are not met.
Here's a thread that I participated in about this.
James Jacobs response was:
"If a class grants you a feat as a bonus feat, you never need the prerequisites unless it says specifically that you do."
He did NOT say "If a class grants you a bonus feat, you never need the prerequisites for the feat you choose unless it says specifically that you do."
Do you see the difference? In his response, he was talking about when a class gives a particular feat as a bonus feat - Like when the Alchemist gains "Brew Potion" as a Bonus Feat at 1st level, even though he doesn't have a Caster Level of 3 yet. Or, how a 2nd level Stalker Vigilante can select Whip of Vengeance as their Vigilante talent, and gain Whip Mastery as a bonus feat without meeting any of its prerequisites.
How do we know a fighter must meet the prereqs of their selected bonus feats? Well, first and foremost, nothing in the class ability says that they DON'T need to met the prerequisites. Unless you have a rule that says you don't need to meet a requirement, you still need to meet that requirement.
Additionally, within the language of the "Bonus Feat" class feature, you find this:
"Upon reaching 4th level, and every four levels thereafter (8th, 12th, and so on), a fighter can choose to learn a new bonus feat in place of a bonus feat he has already learned... The old feat cannot be one that was used as a prerequisite for another feat, prestige class, or other ability."
Since the you cannot remove a feat that was acting as a prerequisite for another feat or ability (including a class ability such as bonus feats) then you obviously still need to MEET the prerequisites.
Lastly, Even if James Jacobs had meant what your fellow player THINKS he meant, posts that James Jacobs makes on his personal account are not RULES OF THE GAME. Unless it is printed in a book, issued as official Erratta, or published as part of the Paizo Pathfinder FAQs, it is just an opinion by a game designer.
Final scenario: my Cavalier gets high enough in levels that he's taken all the bonus feats but Spring Attack. He hasn't spend regular feats on its prereqs. What happens when he gets another bonus feat from his class feature? He can't take the last listed feat, so does he get a bonus feat or no feat?
My understanding is that he can take the feat despite not meeting the prerequisites, but it won't function until he earns the prerequisites.