The origins of the phrase are not clear cut. These two articles cast doubt on Ollie Pickering being the origin.
BASEBALL LANGUAGE IN THE 1890s
It has been often written that the term "Texas Leaguer" comes from the major league debut of Ollie Picketing, who got four hits in his firstgame after being called up from the Texas League. Each hit just blooped over the infield. The next day a reporter who missed a play saw Pickering on first base and asked what happened. "Oh, he just made another one of those Texas League hits," said another reporter. However, Robert McConnell looked up the game stories for Ollie Pickering's 1896 debit, and reports that the record does not support this story.
"The New Bill James Historical Baseball Abstract" by Bill James (at page 69)
The Answer Guy: Origin of the 'Texas Leaguer' hard to pin down
By JOHN MARSHALL, SEATTLE POST-INTELLIGENCER REPORTER
Thursday, September 19, 2002
There are as many theories about that as there are about the JFK assassination. It is agreed that this term for a bloop single into the outfield dates from around the start of the 20th century. But where it came from is the subject of at least a half dozen theories, as recounted in Paul Dickson's authoritative "New Dickson Baseball Dictionary." The Texas League theories range from a team in the Texas League that specialized in the use of the bloop single as an offensive weapon; to the effects of strong Gulf Stream winds on outfield flies in the Texas League; to the debut of Ollie Pickering, either in the majors or the Texas League, who came to bat and proceeded to run off a string of seven straight bloop hits