Renner has a book coming out shortly to explain his theories, so I assume he is holding back the evidence/theories as material for that.
While it's a valid point that it is taboo to lie about death, don't forget that a lot of people do just that. A death in the family requires no doctor's note, won't have people questioning why you seemed just fine yesterday, and hopefully sounds severe enough that people will not question it.
Not saying that's the reason Maura chose to use that excuse - just a possibility to remember.
I had a death in my family during the last year of my uni degree and they asked for a doctors note to enable me to extend my essay deadlines and to cover the time I had off. I had to go to the doctor and get him to sign a compassionate leave form provided to me by the uni. My degree was also a vocational one, just like Maura's so they were very strict about how much time you were allowed off because you could be missing important clinical sessions etc I am in UK though so it may well be different in US. I totally get your point though, but I do question why she did not just say "family emergency" or "family illness" etc.. Why be as dramatic as "death" KWIM.