Rewriting transaction history in POS?

In a POW chain, it requires a lot of computing power and time to re-write the whole blockchain history.

But in POS, it doesn't. It wouldn't be hard to fake all the block producing processes and timestamps and thus all the transaction history to make a 'real' chain like the original chain.

For this issue, there seems to be 'checkpoints'. However, for new network participants, a trusted third party could be required to provide them authentic checkpoint data. Are these third parties used in Ethereum? How are they selected?

Also, between checkpoints, it seems someone could make up a chain (with fake RANDAO processes) where all the cheating addresses are to produce blocks. How is this prevented?