This happens a lot, though nobody seems to bother or probably even notice. Whilst I suppose they're not doing anything illegal, it is misleading and probably a bit naughty, especially if they're making a big selling point of the jam served there being homemade.
It's maybe why the 'Protected Geographical Indication' thing was brought in, Newcastle Brown Ale being an example until they started making it in Tadcaster, then the logo was quietly dropped.
I'm sure there are numerous examples if you look hard enough, such as Scottish Shortbread, sold in Scotland but actually made on an industrial estate in Cleethorpes. Many gift shops sell their own branded stuff but it's just generic produce made elsewhere with their own label on.
The wife once spotted a woman from one of our local farm shop / tea rooms (which proudly advertises home cooked Sunday dinners) buying a bulk load of frozen roast potatoes in Tesco! The Arran cheese thing would have pee'd me off as well.
Visiting the Glenmorangie distillery years ago we spotted an articulated tanker lorry leaving, because of course the whisky is carted down to Edinburgh in bulk to be bottled. Nothing wrong with that but it spoils the image somewhat. The number of beers brewed nowhere near their original places of origin is another one. The modern commercial world eh

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