Competitior's equipment deflects my ball

OK this happened yesterday and I am pretty sure I know the rule but you folks are my jury.

I was with the usually Monday crowd (a league) and we're playing stroke play.  I'm have one of my right to left days and hook an approach to the green which leaves me with a lie in the deep rough (2.5 to 3 inches) on a down hill slope to a green that runs away from me, but I do have some green to work with.  Across the green from me is a 3-4 feet deep trough and I am probably 15 yards from the green edge and maybe 4 feet above the green.  I am thinking at this time that I am going to have trouble keeping the ball on the green.

So I hit shot and it drops into the first cut of the green and merrily rolls along past the pin heading to the deep trough.  Unbeknown to me one member of the foursome left a wedge in the first cut (fringe?) and the ball hits the club shaft and bounces back onto the green.

So here is the question.  I say, since the wedge is owned by a competitor,  I get to play the ball as it lies with no penalty if I choose but could replay the shot at my discretion.  The fellow who owns the wedge says I have to replay the ball and incur a penalty stroke.  One of the other players says no penalty but I have to replay the shot.

So who has it correct?  I think the rule (19-3) is pretty clear on this but I'll yield to the jury.

19-3 is very clear BUT it is the wrong rule.

19-4 is the one you want as it is strokeplay. The other player was not an Opponent but a Fellow Competitor. Rule 19-4 points you to Rule 19-1 which says you play it as it lies.

You only get the cancel option in match play.

Glad to know I scored it correct even if for the wrong rule.   I guess I'll have to start carrying a rule book with me.

I played it correct too I kept the shot because only Tiger or Phil could have kept that ball on the green without a back stop.  So I had no inclination to replay the shot.

I would give the idiot who wanted to penalise you a rule book too. And the one told you to replay it.

Carrying a rules book will probably contribute to slow play.

Does using it to batter your opponent count as proper use?

For that I'd advise using the Decisions.  The Rules of Golf isn't big enough to have much effect.