The 15% doesn't increase the amount of Hive you have, but rather the amount of VESTS you have... but then when you powerdown convert those VESTS back into Hive it can appear as though it was Hive the entire time

That's not how it works. There is price of VESTS composed of two values held in dynamic_global_property_object:

• total_vesting_shares which is a sum of all VESTS from individual vesting_shares balances, which is close to all VESTS in the system (with exception of pending rewards, that have separate counter)
• total_vesting_fund_hive which is a balance holding actual HIVE used to buy those VESTS

That price is used by front-ends to convert VESTS amount into HP.

Whenever user does power up, they transfer HIVE to total_vesting_fund_hive, while they get newly minted VESTS on their vesting_shares balance. Similarly when power down is executed, VESTS are burned, while adequate amount of HIVE is transferred to user balance. Both ways use above mentioned price of VESTS current at the moment of execution. Again - VESTS are minted and burned, but HIVE stays intact, just trades places.

Part of inflation is added to total_vesting_fund_hive thus increasing price of VESTS. The amount of VESTS is not affected by inflation, just existing VESTS are paired with increased amount of HIVE.