Let's see... As far as I can remember, I haven't done anything really detrimental as a facepalm moment, but I have something that's close.
In 2008, I was only acquainted with Pokemon Ruby. Granted, I was 9 years old back then too, and didn't know much about Pokemon aside from what I could see in that game. A sixth grader on my buswould tell me about the best Dragon move: Draco Meteor. He told me that it could be found in Ruby, but it was very difficult to get. You had to go to the Seafloor Cavern and there, if you surfed across the lava, you would get the TM for it.
I checked and I wasn't able to get anywhere near the lava, let alone surf in it. Then he told me that there's a secret passage that leads there. And if you look, there's an egg of a Togepi. In other words... He was telling me that Groudon attacked because it was guarding a Togepi egg.
Groudon the overprotective mother, ladies and gents.
Needless to say, I believed him and searched that cave completely with my newfound knowledge of a secret that none of my friends seemed to know... Because a week later I learned that there was no Drcao Meteor in Gen 3. You can't get to the lava. And Groudon, believe it or not, wasn't guarding a Togepi egg.
Gullible me only lost a few max repels in the game, but I'm pretty sure I lost most of my dignity too.