My understanding is that if a node does not upgrade, then it does not have a way to validate that a transaction is valid (due to being unable to validate the transactions signature), and does not have any way to validate that a block that contains one or more SegWit transactions is valid. Am I right about this, or is this not accurate?
If the above is accurate, then I think you are using a very specific definition of "backwards compatible" to make your statement.
Your understanding is flawed.
Segwit transactions will appear to pre-13.1 nodes as ANYONECANPAY. That's why they will be able to validate Segwit blocks without being able to understand Segwit. This is how any soft forks in the past that alter signature interpretation have handled it, and the mechanism has been in Bitcoin either since the beginning or from very early on.