They reported taking on water beyond the capacity of their pumps and at least one crew member seasick to the point of uncontrollably vomiting blood.
Seems to be well beyond queasy.
If in such a dire state of health I got to wonder why medical treatment was refused once ashore.
As I said before if they were taking on water then that could be a valid reason for a mayday. However if the boat is found afloat then their story wouldn't hold water. Couldn't resist the pun.