It is a slightly ambiguous claim. Taken literally “all AM frequencies” could mean a solid slab of spectrum from about 500kHz to 2MHz. As Chronos alludes to above, this should only mean a slab of stochastic noise. The only useful way of modulating that would be a low data rate carrier modulation - i.e. Morse Code. This isn’t going to be a great deal different to a Marconi spark gap transmitter.
In order to transmit voice you must use a slab of bandwidth for each carrier freqeuncy. For the easy modulation techniques (AM, FM, SSB) this is easy to reason about - you simply have a carrier, and you need eough bandwidth around it to carry the frequency width of the modulation (AM modulation actually nees double this, SSB allows you to use exactly that.) Plus a little bit of space to avoid interference. So in the AM band, you get 3kHz audio bandwidth, 6kHz of radio bandwidth, and a bit of space, gets you to 9kHz spacing for the usual allocation of stations. So transmitting voice, on all AM bands, which suggests a technique that would allow anyone, anywhere, with an AM receiver, tuned to any station, to hear the voice. Which is what one assumes the movie is trying to suggest. To do that you would need to modulate carriers at 9kHz spacing across the AM band with the voice. So, technically it hads meaning, although I doubt it is an off the shelf solution. (Although it would not surprise me to find that some highly paranoid governments might think it worth investion in such a capability to address their citizens.)
Audio modulation of wideband noise won’t work - as you will basically only hear the noise in an AM receiver.