I think it depends on a couple of things 1). the area you are in and 2). the hospital you are at.
Idk how people are defining preceptorship but I think this may be a source of confusion.
The way my school does it is from the beginning of nursing school
until your last semester you attend 'clinicals' - where you go to a specific facility/hospital/unit that corresponds to the lecture class you are taking (med surg 1/2, peds, mental health, etc.). There your clinical instructor will take you to a floor and ask the charge nurse if she knows of any nurses who are willing to let students follow them. Charge will then reach out to nurses who can either say yes or no (most usually say yes out of politeness even if they don't want to) and then the student will 'shadow' them for however long they have clinical. For us we had a different nurse to shadow every day.
PRECEPTORSHIP for us at least was during our last semester of nursing school where my nursing school reached out to a hospital and saw what various units were available and which ones had preceptors. These preceptors (I was at a rather large hospital and my friends at other big hospitals in the area confirmed this as well) had gone through training to become one and get an additional yearly bonus for being preceptors for assisting nearly grad-nurses. And I can honestly say I'm not making any assumptions because in nearly every unit employee bathroom is a flyer from the hospital's HR talking about the preceptor program and what benefits nurses who go through it get.
So while nurses you may SHADOW during your clinicals may not have a choice on taking students, PRECEPTORS are usually given a head's up because of the contract the hospital has to make with your school.
If my school's different/if I've got the whole definition thing wrong please let me know; but this has been my experience.