Natural energy has specific variants (think Naruto's Rasengan).
What do I mean by this?
Well, the natural energy Kurama gathered for Naruto wasn't "based" at all; it was just natural energy. When people enter Sage Mode, they usually absorb a certain variant of natural energy (e.g., Toad and Snake), resulting in their respective Sage Mode transformations and buffs.
This is why Naruto didn't enter Sage Mode, despite being sent a shit-load of natural energy from his biju buddy Kurama – it was plain natural energy.