Ray, I'm not sure why close data could be screwy, but I took your suggestion and used data from this morning when the markets are open, and the same observation holds.

I rephrased the issue below, so hopefully the issue is clearer:

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For SPY, the "share price" plus the Ask of a put is always greater than the strike (otherwise you could make "free money", see below)
For SPX, the "share price" plus the Ask of a put is NOT always greater than the strike (note that there are no "shares" of SPX)

What's going on?

The answer is simple for SPY:
If the share price plus the Ask of a SPY put was less than the strike, then you could buy a share and buy a put and then use the put to sell the share at strike, and get more money than you paid. But arbitrageurs would get to such an opportunity before you, so you'd never see it. And you don't, I demonstrate this using a SPY options chain data snapshot below.

The answer for SPX isn't as clear:
First, the "share price" plus the Ask of a SPX put is *not* always greater than the strike (demonstrated below). At first I was surprised by this, but then tried to rationalize it by arguing that the SPY arbitrage argument doesn't hold for SPX. This is because there are no shares of SPX. You can not "buy shares of SPX" and then sell them at strike using the put and perhaps make money, simply because there are no shares of SPX (SPX has futures and options, SPX has no "shares"). Given that the SPY arbitrage argument doesn't hold for SPX, perhaps it's not suprising to see the relation that holds for SPY violated for SPX options? But it surprised me.

Below is data for SPY, showing that the share price plus the ask of the put is always greater than than the strike:

Data taken 7/29/2024 10:00 AM when SPY=546. Put expiry April 17 2025:
SPY Strike Bid 570 Ask 31.77 33.10  Price+Ask = 546+33.10 = 579.10
SPY Strike Bid 580 Ask 37.60 39.09  Price+Ask = 546+39.09 = 585.09
SPY Strike Bid 590 Ask 44.63 46.24  Price+Ask = 546 + 46.24 = 592.24
SPY Strike Bid 600 Ask 52.70 54.73  Price+Ask = 546 + 54.73 = 600.73
SPY Strike Bid 700 Ask 152.09 154.77 Price+Ask = 546 + 154.77 = 700.77

Below is data for SPX, showing that the share price plus the ask of the put is *not* always greater than than the strike (see the last two rows):

Data taken 7/29/2024 9:50 AM when SPX=5471. Put expiry is April 17 2025:
SPX Strike 5700 Bid 292.40 Ask 293.40: Price+Ask = 5471+293.40 = 5764.4
SPX Strike 5800 Bid 338.30 Ask 339.70:  Price+Ask = 5471+339.70 = 5810.70
SPX Strike 5900 Bid 391.40 Ask 395.70: Price+Ask = 5471+395.70 = 5866.70 ***
SPX Strike 6000 Bid 452.10 Ask 456.60: Price+Ask = 5471+456.60 = 5927.60 ***

Am I missing something, or "don't worry, be happy" and believe the rationalization I'm trying to sell to myself?