But that's not the point here. The point is that you choose an image and verify that it is safe and then pin the hash. So I can pull that hash a thousand times over from whatever source I want and I can be sure it is always the same image that 8 originally verified. I don't care who has it or who now has control over the site because if the image doesn't match the hash, then it isn't mine.
I think yall are using the terminology differently from each other in this thread. "Checksum" historically did not imply resilience against intentional modifications.
Nowadays, it's arguably a best-practice when designing a new protocol or storage format to simply make all checksums cryptographically strong unless there's a reason not to. I think that might be where the confusion is coming from.
The issue is, how do you verify the checksum you are using is valid. If you obtain the checksum from the same place you get the image, then an attacker can simply calculate a new checksum for the malicious image and publish it too.
I guess if you were really sure you had obtained a checksum prior to the service compromise, then that would give reasonable assurance the image was not tampered with.
Checksums/fingerprints can help mitigating the problem of _changing_ images people already use. As you correctly point out they don't solve the problem of authenticated distribution.
Assuming you have fetched a given image and captured its sha in a config file in your version control (e.g. a kubetnetes manifest), then whenever you deploy a container you are sure that you're not affected by exploits happening _after_ you saved the fingerprint.
You create the docker image on your local computer, create checksum and write it down / remember it. Then you just use this checksum when downloading the image from other computers to check it's the same one. This only works for images created and uploaded by you of course, for images created by other people it does not work.
Second preimage mostly, which is harder than collision with most common algorithms (even MD5 might still be secure for this, not that anyone should use it for anything at this point). Collision resistance is only important if someone can create two versions at the same time that have the same hash and wants to quietly switch them later.
Using SHA-256 as you describe works well and is widely used by package systems to ensure that source code being built does not change. Signatures can be better for determining if the initial image is valid if the signing is done away from the distribution infrastructure since development machines might be more secure than distribution infrastructure (and if not you will have problems either way). You still need to get the correct public key to start with. However, if you do have a good image by luck or actually secure enough distribution infrastructure then SHA-256 will certainly let you know that you get the same one later. Signatures almost always sign a cryptographic hash of the message and not the message itself.
I think his point is that for some checksums it could be trivial (and for some, tools already exist). Checksums aren't designed for this, while on the other hand secure hashing is. As a result, authors of hashing algorithms often attempt to mathematically prove their strength and resistance to a collision.