I actually understand both the arguments, and they both hold truth. Hancock did indeed disguise her odd behaviors under the pretense that she's a spoiled brat who has no concern for the well-being of Marines. This pretense and the fact that Luffy's connection to Hancock is completely secret to the world other than Amazon Lily allows her name to be clean. In addition, she was under the close supervision of Momonga.
However, her undertaking is not without risk. She barely avoids being captured by acting like a slob and abusing her powers. Suspicions still linger, though, because some Marine fodder heard 2 different voices in her room as she voyaged to Impel Down. This initial curiosity can become a rumor, which then can be used to suspect Hancock.
The security lapse from the monitor snail being petrified isn't a very clear clue to Hancock hiding Luffy, and can be assumed to be a faulty connection in reception.
But the problem that still remains is how Luffy got into Impel Down. Luffy can disguise himself as a Marine, but imagine how many pirates dare to do that to break out their captains. No one can get into Impel Down without proper clearance and authority. Garp gets in because he has fame and rank in addition to a proof of identity. Hancock has her Shichibukai status and a proof of identity. Other Marines and WG officers can try to get in, but they all need some form of authoritative rank and importance. Anyone from the outside must be escorted through Impel Down, and I highly doubt Impel Down gives daily tours to your average Marine.