Dear friend, usually, when an exchange says "support the hardfork", means that the exchange will support the consequences of the hardfork, so, if there is a split or a multi-split of the code they will give support.
You are right that the statement of Binance is not telling that explicitly but the only meaning, IMO, of the word "supporting" is that.
COINBASE said the same statement giving more details (https://support.coinbase.com/customer/portal/articles/2959951)
Read the last paragraph but essentially they said:
In the unlikely event that multiple viable chains persist after the fork, Coinbase will ensure that customers have access to their funds on each chain.