If the a/c was about to depart, safety first. Escort f/o from a/c for 'medical' check. Slurred speech could indicate brain function impairment due to minor stroke, embolus, alcohol, lack of sleep etc. Same for arrivals.
Let management decide who pays for delays.
If the interview was conducted where non-involved 3rd parties could hear the (false) allegation and not the apology - sue for slander? Certainly poor situation management to reprimand in front of others.
I am all for aircraft safety legislation, but all laws can be abused and false allegations/overbearing authority should be penalised.
At least Yusuf Islam (Cat Stevens) got an apology from the Yanks after being refused entry to US because his name sounded suspicious!