The radiomen on the Coast Guard cutter Itaska reported that Amelia was coming through very loud and clear, but she did not seem to be hearing their replies.
I guess, therefore, that the missing belly aerial was for the receiver.
BTW that clip is not the take off from Lae.
There is a film in existence, though, which is of the last take off of the Earhart Electra, and recent analysis of it shows what looks like puffs of dust behind the plane as it rolled down the strip at Lae. These apparent puffs have been interpreted as the mast at the loose end of the aerial wire bouncing along the surface. The rear belly aerial mast had only a few inches of ground clearance and could have been snagged as the the plane swung around to line up.
I think there is documentary evidence from the time that a length of wire was found at Lae airport after Earhart and Noonan left. It was not merely someone's recollection.