Why are blocks in a permissioned blockchain linked together? My question: Do the blocks in a blockchain without proof-of-work (i.e. a permissioned blockchain) have to be linked together via a cryptographic hash?

Longer version of my question:

(Please correct me if some of my remarks contain mistakes)

The blocks of a blockchain are linked to each other so that after proof-of-work their content cannot be easily faked, right? If several new blocks were created on top of a block which contains my transaction, I can be pretty sure that I'm on the longest blockchain and my transaction can't be faked (i.e. the double spending problem is solved).

However, in a permissioned blockchain there's no proof of work. As far as I know, in permissioned blockchains agreement on the longest chain (i.e. consensus) is reached by having a majority of blockchain participants agree on the longest chain. But since there's no proof-of-work, 51% attacks (pretending to be the longest blockchain while containing blocks with tampered transactions) are much easier to achieve, or am I wrong?

So why would you need to add a hash of the preceding block to a new block in a permissioned blockchain since there's no proof of work and thus linking the blocks in this manner does not provide any help to solve the double spending problem?
I think you're mistaking PoW for a mechanism that guarantees the chain's correctness, rather than just a means for finding consensus.

A blockchain (without PoW) is just an ordered list of batched updates to a database.

PoW is one mechanism to guarantee that everyone eventually ends up on the same chain, but it doesn't guarantee that this chain is valid. Validity is enforced because non-miner full nodes actually validate all the operations in the chain to determine correctness.

If you remove PoW, you need another mechanism to obtain consensus. One way of doing that is having the block by signed by a trusted set of nodes. This means you're trusting those nodes to not sign multiple conflicting chains. However, it does not necessarily mean you trust them to assert validity of that chain. You can still have full nodes that verify that the chain being created is valid. In order to do that, your set of updates must be identifiable. A hash chain is one way of doing that.

If you're going to fully trust whatever your trusted parties sign without any validation, just use a replicated database instead. What a blockchain adds is simply a mechanism for identifying and auditing updates.

To be clear, I don't think there are all that many uses for permissioned blockchain technology, and a lot of the claimed advantages are hype. However, some of them will likely turn out to be a modern instantiation of BFT systems with auditability, and be boring but quite useful.