"I'm curious if . . . it was ever accurate."
The short answer is "yes." Today, of course, it's ridiculous as others have pointed out.
The original electro-mechanical switches were called "step-by-step" switches in the US, or "Strowger" switches in the UK. Later, electro-mechanical switches were called "crossbar" switches.
Both set up a continuous metallic path through the switch which lasts the duration of the call.
In fact, many of the dialing and numbering conventions - dialing "0" for the Operator, dialing "1" for Long Distance, dialing "011" for international, and no area codes or telephone numbers starting with "0" or "1" - directly resulted from the way these switches were designed and wired.
The telephone network was a hierarchical (5-level) network.
Only "Class 5" switches connected to telephone lines - all other levels were "tandem switches" designed to connect two switches together with "trunks". The equipment required to automatically bill calls ("Automatic Message Accounting") was very expensive, so it was usually concentrated in Class 4 or Class 3 "Toll Centers" where it could serve multiple Class 5 offices (and that's why we got free local calling in the US). Row 1 of the SXS "Selector" or crossbar (corresponding to the dialed digit "1") was wired directly to a "CAMA trunk" (Centralized AMA) to a tandem switch where the details were recorded before the call was set up. (Similarly, row 10, corresponding to dialed digit "0", was directly connected to trunks to the operator center).
So tracing a call in an all electro-mechanical network would literally require working backward from the receiving telephone line, to either the originating line (if the call originated in the same Class 5 office) or to the incoming trunk line, etc., etc. But it wasn't "digit by digit." It would be analagous to following a piece of string to its point of origin, then making a note of the telephone number associated with the tin can the string is tied to.
The 1ESS switch was introduced in the 1960s. It was a computer-controlled mechanical switch. True digital switches like the 5ESS and the DMS100 came along in the 1970s.
Digital switching made billing and services like Caller ID a function of software, not hardware, so tracing a call in an ESS network is much simpler. But steppers and crossbars remained in service well into the 1980s, and many were only replaced because the state Public Service Commission required it.
As to any differences between wireline and wireless: let's ignore the radio-based IMTS and talk about AMPS and digital (GSM, TDMA, CDMA). All of these systems were based on digital switching fabric, and all calls were billed (so calling party number was automatically captured), so tracing a call would have been relatively simple.
One additional distinction: there's a difference between information available in the modern network (billing information, tower ID, GPS coordinates), and information shared with the user (Caller ID).