sure, we are exposed all the time obviousily..the sun emits radiation for example..but not all radiation is the same. the sun emmits gamma radiation..wheras plutonium is alpha(I think)..not all radiation is equal.

Alpha radiation travels very (very) short distances due to the large particle size and mass. Unless you inhale or hold an alpha emitter it's not something to worry about. Radon is worrisome because it decays into short lived solid isotopes which irradiate the lungs.

The dose he showed was on average around 1.4 microSieverts/hr. That is 12.25 milliSeiverts/yr One gets 60+ milliSeiverts/yr from smoking a pack a day. A CT scan gives that much radiation. So it's a bit higher than normal, it might be something to question but I wouldn't fret over that.

Lastly, this guy is clearly bonkers and I didn't see him calibrate his instrument so I personally wouldn't believe it.