You'd be hard pressed to find anything absolutely toxin-free. Many toxins have non-linear effects, negligible at very low doses, so there are advantages to diversification.
Even if you could find a handful of foods that are absolutely toxin-free, eating only those would greatly reduce the diversity in your diet.
The obvious optimum is a diet minimal in the effect-weighted sum of its toxins, subject to the constraint of also providing healthy levels of all essential nutrients... which the GP is attempting to reasonably approximate without requiring years of research into the exact diet by proposing toxin risk diversification.
Eating a primarily organic, whole-food, plant-based diet avoids lots of toxins that build up along the food chain, while still offering a huge diversity of foods.
There are far, far, more species of plants to eat than species of animals in human diets.
Right, but it's also "all diets have some level of toxins so they are comparable".
Primarily whole-food, plant-based diets have the lowest level of toxins.
For example, see the Cleveland's Clinic recommendation for a low-inflammation diet which recommends diets like Mediterranean, DASH and whole-food vegetarian.