Not true. Bitcoin is fungible just like cash is.
If I give you $100 in cash and you give me $100 in cash, then the only thing we both need to do is to make sure the dollar bills aren't fake. If they are both legit, then we are exactly where we started from.
If I give you $100 in BTC and you give me $100 in BTC, then the only thing we both need to do it to make sure the BTC is legit. Luckily, bitcoin does that on its own after some block confirmations. So we just need to wait a little.