“Teamwork means never having to take all the blame (yourself)” is a jocular saying that has been printed on many gift items, such as T-shirts, bumper stickers and posters. The saying has been cited in print since at least 1998 and is of unknown authorship.
 
 
7 April 1998, San Jose (CA) Mercury News, “No reason, just policy,” pg., 2A:
Teamwork means never having to take all the blame yourself.
     
NetScrap
Things We’d Like To See On Company Motivational Posters…
Entered on: 09/24/1998
(...)
24) TEAMWORK ... means never having to take all the blame yourself.
 
Google Books
Yada, Yada, Yada.Com.Org.Edu.Gov.Email:
What I Learned on the Www/Internet—Total Nonsense
By Joan E. Miller
Lincoln, NE: iUniverse, Inc.
2000
Pg. 13:
TEAMWORK means never having to take all the blame yourself.
   
7 March 2003, Daily Globe (Ironwood, MI), pg. 3, col. 1:
TEAMWORK…means never haying to take all the blame yourself.
 
25 July 2003, Daily Herald (Chicago, IL), “Good Morning: Dose of laughter is a wise prescription in troubled times” by Jack Mabley, sec. 1, pg. 15, col. 4:
Teamwork means never having to take all the blame yourself.
 
Google Books
Little Book of Office Morons
By Audrey Malone
Cheam, Surrey: Crombie Jardine
2005
Pg. 30:
WANKER
OFFICE MOTTO:
Teamwork means never having to take all the blame yourself.
     
The Press-News (Southeastern Stark County, OH)
TALK OF TOWN
Published: January 12, 2010 11:06PM
(...)
Motto to work by: TEAMWORK…means never having to take all the blame yourself.