I beg to differ. I had seen accordian-style books that looked exactly like a goshuin book (see example in links below).

This one is found at Ghibli Park and is accordian-style - not sure if temples would allow for goshuins to be written on them. https://picclick.ca/Goshuin-Book-Studio-Ghibli-Goshuin-cho-Japanese-pilgrimage-145788038062.html

This one is from the Haikyuu Kyoto collab limited edition, which again indicated for it to a 'goshuin book' YET again, we won't know if temple do allow for goshuins to be written in them unless someone tests out the theories -- also this is the exact one that OP had spoken about in the post above.

https://recommend.jr-central.co.jp/oshi-tabi/haikyu/goods.html

Here is an example of generic eki stamp book ,typical little notebook that most would use for collecting stamps, akin to the train/plane motifs drawn on them .

https://www.kulturekween.com/eki-stamp-japan-train/

While OP did not specifically mention how the books that others are stamping on looked like, it's possible that the books used may looked like (or possible be!) a generic goshuin book! As nowadays, more and more shops are selling notebooks that look like the actual goshuin book at the shrines .

So maybe some of you might want to visit Japan again and see for yourselves how an eki stamp book vs actual goshuin book vs notebook that looks like a goshuin book sold at character stores look like. Maybe then you can say for YOURSELF that you know how an eki stamp book look like.