Entering Jordan from Israel: visa on separate paper instead of passport stamp?

Last week, I went on a guided tour to Jordan (Jerach, Petra) from Israel. I have received a Jordan stamp in my passport, as usual.

As you might be aware, when your passport shows proof you have visited Israel, you cannot enter some Islamic countries anymore. Israel solves this by giving you a piece of paper instead of a passport stamp, however, as the Jordan stamp mentions the name of the border crossing and this gives away I've been in Israel, I cannot use my passport now to enter these countries.

I like passport stamps, so I don't mind having an extra stamp in my passport. However, I'm also interested in visiting Iran for which I now need to get a new passport.

In the hostel I was staying at, some other people went on the exact same tour, but a few days earlier. They used the same border crossing and one of those people was from the same country as me and so had the same passport. The weird thing here: they didn't receive any passport stamp, but got the stamp on a seperate piece of paper.

I've asked our guide in Jordan about this and he said this is impossible and Jordan always stamps passports. However, I've seen the piece of paper with my own eyes.

Is anyone aware of the current policy? When do you get a passport stamp and when do you get a piece of paper?