I have to admit, when I first heard this it sounded ridiculous, but the way you tell the story reminded me of something that made me wonder if in fact, there is any truth in it. Here me out...
I have a friend in Lincolnshire who owns a nature reserve. He has guinea fowl running free on his land. The area has a lot of migrant workers because there's a lot of crop picking to be done and local people otherwise employed or lazy, and not local people don't want to move or are lazy.
So the migrants do the work because the Brits won't or are lazy. My friend, who is a bright fellow with a PhD is convinced that local migrant workers grabbed one of his birds and ringed its neck for their dinner.
These birds are considered poultry, and like chickens, it's entirely normal to eat them. Even if they are your pets. Now his birds had freedom to roam the whole estate and the roads outside. One disappeared on the roads outside.
Now if you think that some of these people come from countries where they probably do grab birds roaming wild, and take them home to pluck and have dinner, it doesn't sound so crazy. But then again, some white folk do that too. But not normally from outside someone's house.
If you are used to catching wild birds for food, then you might well continue to do it in another country, and would that stretch to pets? I can't really say, but it's possible.
I am now wondering whether there is some truth in the rumours that do seem ridiculous, until I thought more about it.