This may sound silly, but are you sure it's an SC?
You may be the 2nd owner, but where did you buy it?
If you got it from a dealer, then definitely go back to them...
They will often try to blame the previous owners, saying that all the keys were not turned in, but that's not your problem...they should be ensuring that all standard equipment items are included when you buy it.
And if you have the PDI, are you sure it's for your vehicle? Compare the VIN's
And this may not be the PDI from the original owners inspection, but from your inspection, before they sold it to you, so of course the keyless is not on there, since you obviously don't have it...what is the date of the PDI...?