Police kill tourist’s cat brought into Iceland Illegally

Sign to Almannaskarð, Iceland
This appears to be a brutal tale of unnecessary cat killing by the authorities but correct me if am wrong.
Why did an Icelandic veterinarian have to kill a domestic cat brought into Iceland illegally? All they had to do was isolate the cat – place the cat in long term quarantine – to determine if the cat was carrying a disease which was potentially harmful to Icelandic animals.
I don’t see a logically need to kill the cat. The cat’s owner could have paid the costs. She probably would have been willing to do so. Did she have the option? I doubt it.
A Swiss woman travelled to Iceland by ship (Norræna ferry). Someone (I presume someone on the boat) tipped off the police before her arrival in South East Iceland.
The South Iceland police found her at Almannaskarð. Her cat – an innocent victim in all this – was taken from her to the nearest veterinarian where he/she was euthanised (we don’t know the cat was killed but I presume it was humanely). It seems that no questions were asked. No quarter was given. No attempt was made to find a more humane solution. Just kill the cat.
Obviously the cat’s owner failed to obtain the necessary permits to import her cat into Iceland. But all animals coming into Iceland are checked by vets and then kept in isolation for four weeks to make sure they are healthy.
Was it beyond the bounds of Icelandic human endeavor to do a thorough health check on the cat and to do it isolation? And then keep the cat in isolation for as long as it takes.
P.S. We don’t have a picture of the cat concerned. Not surprising considering the story.
Source: http://icelandmonitor.mbl.is.