A “thumbsucker” is not a reported news story, but rather is a “news analysis” or a “think piece.” According to the 1980 citation (below):
 
“When a reporter doesn’t have any facts, he sucks his thumb awhile and then he writes down whatever comes out of his thumb.”
 
“Thumb-sucking” has been cited in print since at least 1936.
 
 
(Oxford English Dictionary)
thumb-sucker n.  (a) a child who habitually sucks his thumb;  (b) Journalists’ slang (see quots. 1974 for thumb piano n., 1980).
1891 ‘M. Twain’ tr. Hoffman Slovenly Peter (1935, Ltd. Ed.) 25   Story of the thumb~sucker.
1964 J. M. Argyle Psychol. & Social Probl. ix. 121   There is also some evidence that children who have little opportunity for sucking, either at the breast or at a dummy, are more likely to become thumb-suckers.
1974 S. Alsop Stay of Execution i. 103   Walter Lippmann wrote the best straight think-pieces, or thumb-suckers as they are called in the trade, of any journalist of our time.
1980 N.Y. Times Mag. 11 May 12/4   Slurs like ‘paper pusher’ for bureaucrat, or ‘thumbsucker’ for columnist.
       
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The Nation
Volume 143
1936  
Pg. 594:
The production of such dispatches is known to the craft as “thumb-sucking,” and the products themselves as “think pieces.”
 
Google Books
Walter Lippmann:
A study in personal journalism
By David Elliott Weingast
New Brunswick, NJ: Rutgers Univiversity Press
1949
Pg. 124:
He has done relatively little “thumb-sucking,” the fairly common practice of newspapermen to expound self-generated theories and syllogisms.
 
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Encounter
Volume 16
1961
Pg. 89:
I have seen these stories manufactured out of a typewriter by correspondents worried over an imminent deadline, who couldn’t possibly know the answers—so the non-existent observers, the non-eminent sources, and the non-qualified analysts became the peg on which to hang meaningless stories. There is even a slang phrase for it: “thumb-sucking,” or sucking it out of your thumb.
   
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The New Language of Politics
A dictionary of catchwords, slogans, and political usage
By William Safire
New York, NY: Collier Books
1972
Pg. 671:
A tick-tock (the metaphor, obviously, of a clock moving toward a fateful hour) is often written with boldface dates indicating significant meetings or preliminary events, and is more reportorial than a “think piece” or “thumbsucker.”
 
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Aspects of the Presidency
By John Hersey
New Haven, CT: Ticknor & Fields
1980
Pg. 224:
Hartmann: This is what we used to call in the trade “thumb-sucking.” When a reporter doesn’t have any facts, he sucks his thumb awhile and then he writes down whatever comes out of his thumb.
   
Google Books
Hold the Press:
The inside story on newspapers
By John Maxwell Hamilton and George A. Krimsky
Baton Rouge, LA: Louisiana State University Press
1997
Pg. 50:
Why Journalists Do “Thumb-Suckers”
(...)
To get at those two more elusive aspects of the news, journalists do what they jokingly call the “thumb-sucker.” This is a story that explains the significance of the news. It, too, is found in the news sections of the paper and is written by the same reporters who cover hard news. Virtually every good newspaper is so jealous of its credibility as a source of objective news that it labels these stories news analysis so they will not be confused with hard news.
 
Google Books
The New Partridge Dictionary of Slang and Unconventional English: J-Z
By Eric Partridge, Tom Dalzell and Terry Victor
Taylor & Francis
2006
Pg. 1960:
thumbsucker noun
a long and complex piece of journalism; a writer of such articles US
 
You Don’t Say
Wednesday, August 19, 2009
Our vanishing heritage
Posted by John McIntyre at 9:37 PM
You asked for it: some terms — hardly an exhaustive list — retrieved from newspaper lingo before these endangered print artifacts vanish like the passenger pigeon and the copy editor.
(...)
goat-choker (n.) An article of inordinate and suffocating length, produced to gratify the vanity of the author and the aspirations of the publication. (Cf. Pulitzer-Prize-winner.)
(...)
COMMENTS
LisaMc
Aug 19, 2009 09:15 PM
Love the phrase “goat-choker”—I once had a boss who called such stories “thumb-suckers.”
(...)
John Cowan
Aug 19, 2009 10:12 PM
A thumb-sucker, as I understand it, is a personal-opinion piece, in which the reporter consults his thumb to discover What Really Matters Today. They often appear labeled “News Analysis”, a term which properly refers to an evidence-based summary of the background and implications of a story. Thumb-suckers are generally goat-chokers (a term new to me), but certainly not necessarily vice versa.
   
Laura Lippman
Posted on July 26, 2010
Thumbsucker
(...)
In the newspaper world, “thumbsucker” is the name used for a piece that doesn’t really advance news, just allows a reporter to assemble known facts, often under the claim of “analysis.” I’m not sure why that was the case. “Chin-stroking” or, to be rude, “jerk-off” seem more analogous to me, but maybe I’m missing something. Thumb-sucking is all about self-soothing and very private.
 
Baltimore (MD) Sun
Choking goats, sucking thumbs
February 04, 2012|John E. McIntyre | The Baltimore Sun
A conversation with a colleague prompted me to draw an important distinction in long-form journalism between the thumbsucker and the goat-choker.
 
The thumbsucker, long a journalistic staple, is the article that tells you What It’s All About. Thumbsuckers flourish on Sundays, because Saturdays are generally slow news days and the increased space of Sunday editions is an open invitation to pontificate about the how and why and what next of some development during the week.
(...)
The goat-choker, a term long favored in The Baltimore Sun‘s newsroom, is less an analysis of events than an example of traditional long-form journalism. It is typically an article in which the writer has been given his or her head to proceed at length and at will. It will start on a section front and occupy two or three full pages inside the section. The quality distinguishing the goat-choker from examples of long-form journalism is that it requires of the reader a steely determination, an effort of will to plow through the entire text.