Are monks allowed to travel during the rain retreat? AFAIK, monks are not allowed to be away from their monasteries for more than 3 days during the rain season. But a monk I know had to travel out of the country due to some personal matter during this period for more than three days. 

So I'm curious to know whether there are specific situations in Vinaya where the monks are allowed to break this rule? 

If so, are they capable of receiving the Kathina robes?
It's seven days and only if there is a reason, in a specific (but long) list of potential reasons, mostly pertaining to Buddhist practice. The only true exception I can think of to the rule is the case of obstacles to keeping the rains. As Thanissaro explains:


  Mv.III.9.1–Mv.III.11.13 gives a long list of valid obstacles, which Pv.VI.4 divides into 
  four sorts: dangers to life, dangers to the holy life, a threatened split in the Community, 
  and an actual split in the Community.
  
  http://www.accesstoinsight.org/lib/authors/thanissaro/bmc2.pdf