Battle powers don't have any relevancy to someone who isn't familiar with the system. Freeza told Nail he'd only use his left hand after saying that he'd hold back, so Nail could've taken that as Freeza holding back.
The example with Krillin is more relevant to this situation and I'd be willing to go along with that.
Piccolo wasn't thinking logically. He was thinking of saving Gohan first and foremost, and he'd also gotten arrogant about his standing:
Chapter: 293 (DBZ 99), P4.3
Context: Piccolo talking about wanting to fight Freeza
Piccolo: “My power has vastly increased here! I’ll definitely defeat him! Call me to that planet!”
It wasn't until Nail made him face reality that he realized it was a lost cause to go there as he was.
Given the frequency in which statements like “half my power”, “many times stronger” and such are said, I doubt it.
And Cell didn’t even use his hands to beat Kuririn, but clearly that’s not what he meant when talking to Trunks. Any good fighter can tell if a for is holding back. Even Freeza can tell Goku was withholding the Kaio-Ken, and he can’t even sense Ki.
Hm, that’s possible. In the statement Ryan posted you can see he’s stuttering when talking about his Ki, and Piccolo did sense his Freeza’s power up:
Chapter: 294 (DBZ 100), P14.1
Context: as Freeza powers up
Piccolo: “That large ki has become even more absurdly large! Is this ‘Freeza’ finally starting to move?!”
So he was indeed being delusional, regardless of how he compares to Freeza. This is like when he wanted to save Gohan from Cell in the Cell Games.
@Diamond Ryan he’s not referring to Freeza’s power when calling him a monster though. But saying his Ki is outrageously large works to the same effect regardless.