Normally I use Gritless hand cleaner {I use E-Z-GO as Go-Jo seems to not work as well}and it will not remove the paint. Rub it on and wait about 10 minutes. Use a tooth brush to rub it in a bit and rinse with warm water while tooth brushing.
He can try Acetone also which should leave the stain and paint. The only reason the paint would come off is it was painted onto the oil at one point but normally it is on dry wood. Hope this helps. Rick B
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If I cant fix it,, It must REALLY be broken!