Spinach is a plant. All plants contain elevated levels of potassium (compared to meat and other animal-based food). All potassium contains K-40. K-40 undergoes 1.3 MeV beta decay 90% of the time and 1.5 MeV gamma the other 10% (IOW: K-40's decay energies are not low, they are stronger than Cs-137!). Eating any plant, you are getting yourself exposed to internal radiation from K-40.
Radium is an alkaline earth element. Those are pretty mobile. Radon is a noble gas - much more mobile than radium. Both will escape from fractured rocks which contain elevated levels of uranuim; or places with significant geothermal activity. Radium in water you drink will be deposited in the bones, since it is chemical analog of Calcium.
So, sorry to burst your bubble, but we do experience *internal* exposure to radiation from natural sources our whole lives.