Transformations. It's posible that what Babidi and Dabura could feel were the lowered base powers of the Saiya-jin's + the full of their SSJ powers. (What I mean is what their power as SSJ's would be if their lowered base PL was their actual full power.) Where as Piccolo has no tranformations they would only sense his lowered power. This is just one of dozens of explantions.
This is an assumption, though. What the evidence here shows is that Babidi and Dabura can tell Vegeta, Gohan, and Goku are stronger than Piccolo in their base forms. Since they don't know the Saiyans can transform, they likely don't know their full power. You say what's POSSIBLE, but it's not like Babidi said, "Hey Dabura! Those three dudes with blackhair have secret transformations of which I sense the energy of. The green one's a puss, though." What you say may possibly somehow be what is true, HOWEVER, the fact that the three Saiyans were in their base forms would indicate the opposite. You can theorize, but what's there is what's there. It shows the three Saiyans in there normal forms surpressing their power, Babidi and Dabura sense they're stronger than Piccolo.
No one's really provided any real evidence FOR the Saiya-jins having PL's beyond that of Piccolo while in their base forms. The only thing that even remotely works in favor of that is the Vegeta blast against Cell but that's nothing definitave. James even pointed out Krillin and Gohan handling Ginyu while he was in Goku's body. There are numerous times when people considerably weaker than the other person has done some damage, or at least been an annoyance.
Piccolo couldn't approach Cell. He got blown away. Vegeta could, even after he had the shit slapped out of him by a "SSJ2" Cell.
Why are Dayspring and I the only ones that can see what the evidence shows?
Because you have theories, not hard evidence. You claim that Babidi and Dabura MAY have sensed the Saiyans' SSJ Ki, but there's nothing to show that. That's all nice and good, but what the manga and anime show us is that Goku, Vegeta, and Gohan are in their normal forms, and Babidi and Dabura sense their current powers. You can hypothesize, but until you show something from the manga or anime that totally proves otherwise, then I can't really change my opinion. The evidence FOR the Saiyans surpassing Piccolo was from the manga, not my head. It's there in (literally) black and white.
Because this time was different. Every other time he unlocked his powers it merely raised his strength for a few moments, and only while angry, then it would go away again. This time it fuled his tranformation into SSJ2, it didn't temporarily raise his power. And gaining a new transformation dosen't power up a person's base form.
After Gohan learned to fight, there's no true indication that he DIDN"T keep his power, he was usually just quickly outclassed after becoming angry, whether it was the Ginyu Force or Freeza.