Not that I have ever been a fan of Passive Perception, but I think Crawford's advice it's one valid option (but definitely not the only one).
The way I've run perception so far is
technically without using passive perception, but
practically many times I just let the character succeed, if I think something is just impossible to miss, especially as a group.
I don't think there is only one "right" way to handle perception. These are just equally valid options:
a) Always roll, unless you notice that even a natural 20 would not beat the DC or a natural 1 would always do. Ignore Passive Perception.
b) Roll sometimes, grant autosuccess or autofailure some other times, based on narrative. Ignore Passive Perception.
c) Roll sometimes, use Passive Perception some other times, based on narrative.
d) Always use Passive Perception when it's enough, roll only when it's not enough (Crawford's method).
Crawford's method is quite simple and regular, so it will work well for gaming groups which
don't like the DM to make subjective rulings.
You know the general location of invisible creatures!
JC says that being invisible and being hidden are not the same thing. Invisible creatures give themselves away by making noise and interacting with the environment. Invisible creatures need to use stealth or have some other cover to be hidden. A monster or PC might be distracted or lose track of an invisible creature, but if you know someone is likely to be invisible and are trying to find it, you have a general idea where it is. He says that the game mechanics make invisibility awesome enough on their own - advantage on attacks, disadvantage on attacks against you, can't be targeted by spells that target "a creature you can see" - so invisibility does not need any additional benefits. I wish the DM who hammered away at us last weekend with the unseen, completely silent, unfindable shield guardian hadn't made us swing randomly at thin air until we got lucky and found it because he said invisibility made it impossible for us to know where it was.
I don't think your DM did it wrong. It's true that invisible doesn't automatically mean you don't know where it is, but IMHO this is too much situational to be blanket-ruled like Crawford suggests. "Invisible creatures give themselves away by making noise and interacting with the environment" is simply false in the general case, since a creature
doesn't have to make noise and interact with the environment all the time! You can of course decide that the creature needs a Stealth check to avoid making noise and interacting with the environment if you want, but for most creatures it's hard to believe that simply standing still would not be enough to avoid the (typically large) probability of failure of a Stealth check.
Even in combat, where it's more reasonable to say the creature can't avoid noise and environment interactions, it's totally fine to rule that an invisible creature is not automatically pinpointed. It just depends... probably easy to know where it is if you're on sand or mud, but if you're on a solid stone floor? What if the creature is flying or hovering? I don't think I'd even allow opportunity attacks against such an invisible opponent.
If passive scores are always the floor of rolls, rogue's reliable talent would be useless... trying to wrap my gead around that...
If
really "your perception checks can
never be worse than your passive perception" is meant literally, then you are right and Reliable Talent is useless for Perception.
If the above rule is intended for
every ability check and not just Perception (considering that the PHB passive checks rules aren't limited to specific skills), then Reliable Talent is
always useless.
On the other hand, the PHB says about passive checks: "Such a check
can represent the average result
for a task done repeatedly, such as searching for secret doors over and over again, or
can be used when the DM wants to
secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster." The focus here is on something repetitive/routine (like being alert for hidden monsters all the time), so at least it doesn't suggest to use passive checks always. At least not for a lot of skills! Disarming a trap, socially interacting with NPC, performing an athletic or acrobatic stunt and various other skills are practically never repetitive/routine, they are instead always ad-hoc with a specific current target.
Skills that are naturally repetitive (or "passive" as in "active all the time") are pretty much only Perception and Insight. You might arguably also advocate that knowledge-type skills are also active all the time, although knowledge skills have their own special implications when allowed to use passively (basically granting a potentially massive amount of knowledge to everyone, which is why I normally always require rolls for knowledge and often just declare an autofailure if non-proficient). All other skills are rarely if ever repetitive, so Reliable Talent should stay safely useful even when using Crawford's approach, just not for Perception and Insight.