Verb for looking at someone's newspaper or phone stealthily

Shoulder surfing has a negative connotation.

Wikipedia says:

In computer security, shoulder surfing refers to using direct observation techniques, such as looking over someone's shoulder, to get information. It is commonly used to obtain passwords, PINs, security codes, and similar data.

You are reading over their shoulder, even if it doesn't actually involve reading over their shoulder because they are sitting next to you on the train. "Over someone's shoulder" is a set phrase. It has the negative connotation of a surreptitious act.

OED includes shoulder surfing, for example "The librarian wouldn't punch in the ID and passwords if you were looking over her shoulder, trying to shoulder-surf," (my emphasis) but as Chenmunka comments on the question, it's normally used for [and the OED defines it as] "the practice of surreptitiously watching a person who is using a computer, cashpoint machine, etc., in order to obtain confidential information, such as a password or personal identification number, for fraudulent purposes." Note that even that doesn't actually have to be physically looking over someone's shoulder, merely being positioned to view the information.