Yes, this is true. P-Max uses data from the search campaign to help it determine what search queries to target. Sometimes Google even calls P-Max a search campaign companion.
That said, Google recently introduced P-Max keywords (max 25 broad match) as part of asset group targeting options. This is still in Beta. It could be that at some point Google announces that it’s no longer necessary to run search campaigns alongside P-Max.
There are other benefits to running search as well such as getting valuable query data and a deeper understanding of what’s driving performance.