We must remember we're talking about a few dozens of antiatoms here. The few gamma photons they turn into when annihilating are so utterly insignificant compared to natural background radiation it isn't even funny.
Not to "actually" here, but actually... while positron/electron annihilation results in just photons most of the time the situation with anti-proton/proton annihilation is much more complex. Initially you end up with a bunch of high energy pi-mesons (you can think about this as the quarks and anti-quarks pairing off, which isn't really correct since typically more than just 3 pi-mesons result from an annihilation, the typical number is about twice that). These then decay into showers of other particles. Photons, certainly, but also leptons/anti-leptons (muons and electrons) and neutrinos.
In terms of intensity you are absolutely correct though.
