What the use meant is how do we know that the Bitcoin we are buying in the exchange actually exists....
For example, when you purchase Bitcoin in XXXXXXXX exchange, how do you know if you have been credited a number (a simple number in their database) OR a real Bitcoin (1.00000000 bits)...
Essentially who is to say that they are not faking the existence of Bitcoin in their exchange in order to increase the volume... And you make a point, we have block explorers for that, but with so many addresses an exchange has it is difficult to calculate if you do not have access to their ledger...
Short story, there is no way to be sure, UNLESS they are being Audited frequently....
Actually an exchange is a place of buying and selling bitcoin, so definitely there is no fake bitcoin in the market circulation, people might have earned it by trading or purchased it using their debit card from fiat currency, so there's no way a fake coin could be purchased on exchange. Moreover, if its actually fake, blockchain has an explorer that reveals all bitcoin balance shown on the address which makes every transactions to be transparent, easy and accessible.
And also beware of exchange that lied to investors, some provides fake volume and liquidity which were proven to be faked at last, so if you really want a good exchange that won't give a lie about them, you could consider binance, huobi, okex and other top exchange as directed by coinmarketcap.