I don’t doubt your friends believe 3 is the max allowed. More than likely it’s a bad culture and mindset adapted and engrained from the regionals. The average regional pilot accumulates 36 -50 hours of sick time in a year (enough for 2-3 4days). The most junior Delta pilot is about 4th year which equates to 125 hour of sick time per year. It gets better. From year 9 to 20 and beyond a Delta pilot accumulate 240 to 270 hours of sick time per year.
I highly doubt 3 sick calls per year is out-of-bounds. I work at a regional and I get where you are coming from, however, it is unrealistic for anyone to expect you to only be sick 3 times per year and anything over that is too much.
The regional mindset and culture on sick and fatigue goes against everything you learned as a early as a student pilot from primacy IMSAFE..
I’m not saying one should burn through every hour of sick time they accumulate in a year, however, it is crazy that pilots have adapted this unsafe practice which is now the new norm.