This thread explains most of what you need to know about labor rights in the event of a family member's death.
The question right now is, can the employee take time off before the death occurs?
Art. 7 of the Regulations of Leave-Taking of Workers states that you can take up to 14 days of personal leave (shijia) per year, unpaid, when necessary. Art. 20 of the Act of Gender Equality in Employment states that you can use up to 7 of those days to care for a family member.
These are the minimum standards that override anything lower (or missing) in a contract or work rules.
Note that Art. 10 of the ROLTOW recognizes that in an emergency it may not be possible to go through all the formalities immediately. That doesn't mean the employee loses the right to take leave.
If the employer demands evidence before agreeing to the personal (family care) leave, an email (from the hospital ideally, but from anyone if there isn't time) should be sufficient. If that doesn't satisfy the boss, well, I would be inclined to say see you in court.
Applying for mediation through the labor department usually takes a few weeks, but they can give advice immediately.
Btw, I would document absolutely everything. Being able to prove they're a bunch of, um, insincere people technically doesn't count for anything, but it doesn't count in their favor either. And if they've been that insincere already, there's no telling how far they'll go. (What, his father died? When? )