There was a little incident several years ago where a worker with low levels of contamination somehow left a nuclear power plant without the monitors alarming. It wasn't the plant I worked at but we studied the incident report in continuing training class.
Anyway, the worker flew across country to another plant for a contract assignment, staying in two hotels in the process, used taxis, a rental car, the whole nine yards. The 2nd plant discovered he was 'crapped up' (as we call it) and notified the 1st plant where the contamination had occurred. The 1st plant had to send a team of technicians to do contamination surveys all along the travel route, including tracking down the airplane and surveying it, the taxis, the hotel rooms, etc. Took them two weeks. They didn't find anything above background levels, and most definitely didn't march around in protective clothing and masks. The contamination was fixed in the person's skin and apparently didn't come loose from what they could tell.
Not to scare anyone, but you never know. The person sitting next to you could be radioactive from medical treatments, such as for certain heart tests. Or they may have Cobalt-60 seeds inserted in their body for prostate cancer treatment.