Wrong. As usual.
Here is the last one (that I could find):
June 30, 2005 Houston Astros at Cincinnati Reds Box Score and Play by Play - Baseball-Reference.com
Here is a famous one:
New York Yankees vs. Baltimore Orioles - Recap - September 18, 2003 - ESPN
Most ties in a season is 10 by the 1904 Tigers.
Most ties for the history of a franchise is 163 by the New York-San Francisco Giants 1883-2013