That's not accurate. Connecting to your own node does mean you won't be querying Ledger's nodes for your transactions and balances, but Ledger Live still collects a whole ton of other information and phones that home to Ledger entirely separately.

The best option here is to not use a Ledger device at all. The best way to use a Ledger device (other than through an entirely airgapped computer) will be with non-Ledger Live software such as Electrum or Sparrow, which in turn is connected to your own node.