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I think the gap between you two is that you are describing the "biological half life" of tritium while using the term "half life" to exclusively refer to the "physical half life". In Health Physics the distinction between the two is very important and generally once you start talking about the effect on people it is best practice to always clarify which one you're talking about.
The biological half life of tritium is also a little more complicated than "12 days", it depends on the form it is in. If inhaled as water vapor it almost immediately gets re-exhaled, whereas if drunk as liquid water it can be ~10 days depending on the person's water turn over (<8 hours if dialysis is used for treatment following extreme exposure) ... tritiated water is one of the few things that you can speed up the elimination of by drinking more water. For tritium bound up in organic molecules and ingested (food/fish) the biological half life can be closer to 40 days.