Slow Drain

Quick question. We sometimes have slow draining in the sink. Sometimes the garbage disposal side will drain extremely slow and turning on disposal will cause water to come out in other sink. I’ve snaked the drain to no help. Trap is for sure clean.

I had a plumber put eyes on this when he was out running a new gas line. He took one look and said it due to how low the drain is on disposal side. Meaning I would need to open wall under cabinet in order to fix permanently. Does this pass the sniff test or is that bs?