So firstly, only ITM puts have a low implied volatility relative to ITM calls. ITM puts and OTM calls must have the same IV due to Put-Call Parity. Negative IV skew exists in indices such as the S&P500, NASDAQ, etc where OTM puts and therefore ITM calls (Put-Call Parity) have a greatly higher IV relative to ATM IV and to the IV of OTM calls and ITM puts.
Although each product you look at will have a different shape of its respective implied volatility curve, so that must be taken into consideration when determinting residual PnL.
If you are long an ATM delta-hedged SPX call, your PnL will actually not just be dependent on whether the underlying realizes more volatility than the implied volatility you bought it at. In other words, your profits AND losses will not just be made up from the profits and losses from continuously delta-hedging (gamma profits outpacing losses from theta).
This is due to the existence of "skew delta" or "shadow delta". Under Black-Scholes, implied volatility should be constant across all strikes. But obviously that is not the case in the real-world due to existence of skew. If you go long an ATM call or put in general, and then delta-hedge to 0 right after, you are actually (most of the time) either long or short some extra deltas.
Why? Because if the market slides down, your fixed-strike call will have slid and moved to the right of the implied vol curve where it picks up an implied vol of the OTM calls, which even lower than ATM vol. You will lose the change in fixed strike vol * vega.
Now add in another factor. If there is an increase of X vol points to the entire floating vol curve of your tenor (aka your call option along with every other option on the chain gains 1 or 2 vol pts) the (vega) profits from that may have outpaced your fixed strike vol losses.
You will have residual PnL from being long/short extra deltas than you should when your Black-Scholes delta would tell you otherwise.
The spot and implied vol correlation, and whether or not the market is following the sticky delta or sticky strike dynamics, must be accounted for nowadays or you will be wondering about where you extra profit, or in most cases, losses came from due to residual Greeks e.g. shadow delta, shadow gamma and so on.