There's a similar doubt with the inclusion of Manu NP in the 'No road access' connection.
Jarek sent me this: "In fact Manu -at least the southern part - is fairly easy accessible by road (Paucartambo - Pilcopata), the road not paved but in good condition crosses National Park boundaries, there are signs of".
Looking at the maps, I believe that this road straddles the Southern border of the park (runs parallel to it for some time). The so-called Cloud Forest though, which it cross-sects, is outside of the WH core zone.
As per wiki: "the only direct access to the lowlands is by boat, up the Manú River. This singular entry point is easily patrolled by park guards. The road Cusco-Paucartambo-Shintuya borders the southern section of the park and provides access to high-Andean ecosystems"
So tentatively my conclusion would be: you'll certainly will be able to see the park from that road (and maybe put your feet in there), but there are no roads inside the park borders.