Sounds like there may have been something in the mud that has caused the staining, as I wouldn’t have expected ‘ordinary’ mud to do this. Does your neighbour remember where the mud splatter might’ve happened?
If your neighbour had been driving on country roads, I’m wondering if there was farm animal poo in amongst the mud that might’ve reacted with the paintwork; mud and waste from farm animals could be present on country roads if the animals need to be moved from grazing pasture to farm buildings on different sides of a road. We all know that bird poo reacts with clear coat - and if birds have been eating dark coloured berries, paintwork staining can happen - so there’s a chance that a mud and farm animal poo mix could also stain.
You or your neighbour could try claying the affected areas, or even try a tar / glue removal product to see if they have any effect on the stains (they won’t do any harm to the paintwork). However, it’s likely that machine polishing would be the best option - starting with a finishing polish with little or no ‘cut’ on a finishing pad. It that doesn’t have the desired effect, then move up to a slightly more aggressive polish and pad combination.
It might be worth your neighbour checking out the local professional detailers in your area for a professional opinion - they may be prepared to ‘correct’ just the area(s) that are affected by staining and if so, it shouldn’t be too expensive to sort.
Let us know what the outcome is
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