When I first started teaching, I would generally believe students when they said they missed class do to a death in the family or some other dire circumstance. Sadly, I soon found out what should have been obvious: people will lie about terrible things for rather small reasons (like making up a test).
Since my grandfather died when I was in college, I understand how that can affect a person and hence I am sympathetic. However, like most professors I have noticed the convenient death syndrome: near relatives dying right around test dates and paper due dates. While death is a serious thing, I have often joked that professors should send out warnings to students relatives about our exam and assignment/paper dates and the alarming correlation between these dates and deaths.
My policy on excuses involving deaths (or alleged deaths) has been to express sincere sympathy and then request documentation. I still feel a bit bad about asking for this (“oh, someone you love died…well, prove it…”). But, I’ve found that good students who suffer a death in the family generally show up at my office and have the documentation already on hand.
For students who lack documentation, I have a “mercy” policy: each student gets a “mercy” that can count as a “no questions asked” excuse for a missed exam or late paper. I did this mainly for two reasons: 1) students do sometimes have legitimate reasons for missing class that cannot be documented and 2) I feel bad when people lie to me.