In 2008 there was a banking scandal and there was a run on the banks because knew that they could not access their money. Yesterday Bitfinex has a scandal and everyone with their own keys just smiles.
https://cryptostar.money/blog/bitfinex-scandal-bitcoin-stops-bank-runs/
https://cryptostar.money/blog/bitfinex-scandal-bitcoin-stops-bank-runs/
The problem with Bitfinex is that some people suspect that they use Tethers to manipulate Bitcoin's price, so even if you control your private keys, it still affects you, because it negatively impacts the price. The value of Bitcoin as store of value is being undermined by shady ecosystem. Hopefully Bitcoin today is more mature than when it was during the Gox fiasco.
OP is not saying that the clamp down of Bitfinex is not effecting the Bitcoin price, he is saying that people with "only access" to their private keys are unaffected, because they can still access their own coins, because they are not sharing the access with any centralized service.
This is why a sudden "Bank run" or "Exchange run" will not affect people who are not sharing access to their private keys. A centralized service can block access to people's accounts in times of panic, but this cannot happen if you own and manage your own private keys.