Someone better not tell this guy that cell towers are omnidirectional so he'll experience that radiation regardless.
But the radiation is subject to an inverse-square law. A high-power source at a considerable distance (the tower) can give this guy less radiation than a low-power source at a close distance (her cell phone), as Opportunist's dad pointed out.
As an example: the guy is probably in a near-rural area, if he's trying to get away from radiation, on the outskirts of town. In hilly country, Wikipedia says a rural area can get a maximum of 5-8km. Let's say he's 5km away. (This is Santa Fe, so it's not exactly hill country, but it's probably not exactly totally rural either.) Let's also say the tower is using the regulatory maximum of 2000W output. (Most use much, much less, and I don't remember if modern cell towers are even allowed to use 2kW. But it's no more than that.) Using I=P/(4*pi*r^2), we see that the intensity at his house from the tower is 6.37 uW / m^2.
Her cell phone, if it's GSM, is capped at 2W output. The article doesn't say how far apart their houses are; just "on the next block". I'm going to just guess 150m away. (Manhattan blocks are 80m x 200m; central Melbourne blocks are 100m x 200m.) Using the same formula, the radiation intensity from her cell phone is 7.07 uW / m^2. With this set of assumptions, her cellphone could be irradiating him more than the tower (at peak; of course, she's probably not continuously on her phone).
The actual numbers are probably vastly different; different assumptions can change these by orders of magnitude. I'm ignoring modern cell realities, too: cell towers tend to be much lower power, but closer together these days. They also tend to use a non-uniform radiation pattern, not wasting power by radiating cell signals at the birds. Cell phones rarely radiate 2W of power. There's lots of other stuff that means that my numbers aren't anywhere near right, but it does demonstrate that it's POSSIBLE that her cell phone gives him more radiation than the tower.
Then again, the sun provides 750 W / m^2 to the ground (after atmospheric effects), a hundred million times more intense radiation (remember, my other numbers were in microwatts per meter squared), and at higher frequencies. So yeah.