As long you 100% sure that they ain't cooking/mixing it with haram stuff, my assumption was yes, you can. Though if there is even a 1% of uncertainty, you should not.

so muslims keep a record of all transaction, exchange of notes and coins of the people they do business with..?

last i checked most hypermarkets have a non-halal section. I guess those muslims that shop there are sinners then.

Some muslims are really paranoid about halal thing.