Earlier quoted context omitted.
I think your post needs to clarify this is true only if you use the ipfs client to access things hosted on ipfs. Accessing ipfs.io/ipfs/ doesn’t do anything you mentioned. Its just a gateway. You could take the link on the main submission. And replace ipfs.io with any (most, because some are offline) of the links here https://ipfs.github.io/public-gateway-checker/ And it will still work.
That's true, and I should have clarified that. However, is using a proxy like ipfs.io really using ipfs? If everyone did that, there's no point to using this protocol. The strength of the network comes from the fact that the content gets replicated/distributed when accessed. That doesn't happen when accessed through a proxy.
Yes! Because the gateway can go down and you can still access the content via local IPFS node or by using another gateway.