Found a 65-2, 3", that is recessed but not pinned---is that strange? Or was there a transitional state where they pinned some of the 65-2s but not others? Those of you that have these can you tell me what the deal is---or should I assume that the gun has been rebarreled (but even that doesn't make much sense since I saw no hole on the frame for the missing pin---and yes, I realize that this might be nonsensical). Or given that I haven't seen but one 65-2, perhaps they all came recessed but not pinned.
Again, only you knowledgeable guys would know.

It's not unusual for there to have been a transition period during any changeover. You might find pinned and not recessed, or recessed but not pinned.

I've had a couple in my time. I don't remember which ones specifically though.

__________________
John 3:16 .

To add to Cajun's thoughts, M65-2 should be P&R, the M65-3 should not, but as the changes were made, some -2's would lose one or the other trait, while -3's might still have one or the other.

As you said, "transitional". Fairly common among all models that were P&R at their start.

One of my favorites is a unfired one owner 41 magnum nickel. Has all three boxes, shipping box, blue box, and wood presentation case still in the shrink wrap un opened. Inside is a big honking 8 3/8 that shines like a mirror. It is a model 57 no dash, but yep, no pinned barrel. I missed it when I bought it, now I am fine with it.

Model indicates pinned and recessed, but like others have said you get the transition guns. I don't think the factory thought anyone cared one way or another at the time.

Typically a revision change denotes there was something changed that involved a new different part, if the order to cease the process of pinning the barrels came down just prior to the order to cease recessing the chambers of Magnum revolvers that change alone would not trigger a revision change as no new part changed, if t came down at the same time the revision change would not take effect until the supply of recessed cylinders was exhausted since the factory did not waste parts.

This means for instance that there are transitional model 27-2 revolvers that have recessed cylinders that were still in inventory but no barrel set pin,
since there was no "part" change yet they would be marked as 27-2, when the recessed cylinder supply ran out the ones that got the new non recessed cylinder were marked as 27-3's.

While I haven't studied the model 65 closely it should be the same scenario that you will find a non pinned 65-2 with a recessed cylinder but you would not necessarily find a 65-3 with a recessed cylinder
Of course rule #1 with S&W is never say never as anomalies do occur.
On a side note my bet Is if you removed your barrel it will have the cross cut for a set pin.