Yes exactly. So by running a node I can point my wallet to my own node to check my balance and transactions without concern about fakery going on or prying eyes watching.

Additionally nodes enforce the bitcoin rules. If a transaction didn’t follow the rules then my node doesn’t add it to the blockchain records. All the nodes talk to each other making sure everyone has the latest blocks of transactions and that everyone is following the rules. If someone puts out new bitcoin rules I have a choice if I want to use that or stay with the old ones. It’s the consensus of everyone independently deciding what rules to use is how the network updates and defends itself.