Well, fiat money is considered to be fungible, yet it has the same concept of taint. Entities like banks or some companies can freeze and reject transactions if they deemed as high risk by their algorithms, for example coming from a blacklisted country. Or when a person with no financial history suddenly deposits a huge sum in cash.
That's a good point actually. I never thought that electronic fiat is non-fungible. 
Well it's a bit more complex than that. A grocery store won't be doing any background checks and asking for proof of income, so in that situation fiat is fungible - a criminal can walk in with a stolen credit card and pay with it. But generally when doing large value transactions your bank will ask about the source of your money if they have a reason to - like if you are getting $3,000 paychecks every month, and suddenly deposit millions in cash.