Is it permissible to have sexual intercourse on the eve and day of Eid, whether it is Eid al-Fitr or Eid al-Adha?

What you heard from some brothers and friends is incorrect. Intercourse on the night of Eid and during the day of Eid is permissible. It is only forbidden during the daytime in Ramadan, or while in a state of ihram for Hajj or Umrah, or if the woman is menstruating or in postpartum bleeding.