Yeah, I thought the same thing--and even looked at his 2003/2004 gamelogs to confirm! Even in the year he had 232 walks, though, he still didn't have a streak as long as Cullenbine's.
22 games in a row, by Roy Cullenbine in 1947:
http://www.baseball-reference.com/players/c/cullero01.shtml
Game log:
http://www.baseball-reference.com/players/gl.cgi?id=cullero01&t=b&year=1947&share=2.25#1097-1118-sum:batting_gamelogs
If Kendrick misses a significant amount of time, Trout might not see another hittable pitch all year. While I'm happy to see him getting on base, all of the walks are getting a little boring.