There is no safe minimum dose once it is in your body, slowly disintegrating, radiating into your organs and cells.
There is also no safe minimum exposure to sunlight, no safe minimum amount of air to breath, no safe minimal exposure to germs, no safe minimal ingestion of food. Nothing you do is safe.
There is no safe level of ignorance either.
But, if your definition of safe is something that is unlikely to cause any harm or ill effect, then small radioactive doses, internal or external, are quite safe, particularly in comparison to many things that we do in everyday life that we consider safe.
You are incorrect. Small doses are highly toxic because the meabolism transports them to sites around the body where they continue to emit radiation and gestate cancer. Oppenheimer's own research found pu-239 to be fatal at 1-10 micrograms, toxic as an inhalant or when ingested. So your statement contradicts even the 50 year old science.
As for energetic levels, and depending on the radio-isotope analogue, if they are beyond a certain level they are cancerous, if they are below a certain level they are mutagenic to the DNA and cause transgenic disease. So, no, there is NO safe level of exposure just whether you or your progeny experiences the consequences.
As for your "comparison to many things that we do in everyday life that we consider safe", any risk of exposure is measured against the severity of consequences. An argument like that presupposes that you have control over your exposure to the risk, which you don't have with radio-isotope exposure in the foodchain. The difference with Fukushima is that the risk is being increased e.v.e.r.y.d.a.y and no-one has any control over that exposure anymore.
This leads to the fundamental point missed in this argument. WHOI, with a small budget detected C137 of the coast of the US with just 50 samples from the pacific ocean. No government funding, one boat and a small group of dedicated scientists. Should we just assume that the rest of the ocean is hunky dory and "just the bits they were checking" happened to have radioceasium in it?
That is why there is no safe level of ignorance.