Probably the OP means that the bought bitcoins were considered, as they call it, "dirty"
Today, there is a lot of information about what "dirty bitcoins" are and how not to get caught buying such coins. Probably already from the name, it is clear that they include bitcoins, which were involved in any fraudulent activities, and all those who have anything to do with them are taken into account by the investigation services.
As for the exchanges, if suspected, they have the right to freeze funds. The verification is well done by Chainalysis, which has the Chainalysis KYT product. With its help, the past of cryptocurrencies is revealed. But it is unfair to blame a "bona fide purchaser" who has nothing to do with criminal activity.
Yes, if you're buying from another person directly, there will always be a risk that you will receive some very directly tainted bitcoins, the risk may be very small, but it's there.
But with centralized exchange all the funds are pooled so the users won't have to deal with it, the authorities will contact the exchange. Unless the exchange is laundering money and will itself get shut down, like it happened to BTC-E.