When you say "core units", do you mean that in the sense as the term is used in Army Forge? If so, the Great Leader benefit doesn't work since Hero is a separate category from Core Units so a hero on their own would never be able to claim an objective that is "accessible to core units" only. Either way, I don't quite see the point of limiting which units can claim objectives here.
Viewing post in Infection Invaders (Mission Jam, Last Second Entry) jam comments
The language addresses terrain placement, not unit capture rules. "Accessible" meaning that since players may be able to place terrain or objectives competitively, and that objectives may be placed in a way that prevents vehicles/monsters from reaching them, they absolutely cannot be placed in any way that any infantry type unit would not be able to reach the objective. Thanks for the clarification.