Maybe they shouldn't be called that

Craig Biggio's 1997 Houston Astros hold the modern team record for most HBPs in a single season, racking up 100 that year. This year's Dodgers look to be making a run at that record. With 24 plunks in 39 games they're on pace for 99.7 over 162 games.
The '97 Astros 100 HBP season ranks 8th all time but the 7 seasons ahead of them all occurred before 1900. 6 of those seasons, including the all time record 160 plunk Baltimore Orioles, prominently featured Hughie Jennings.

On the other side of the equation, the World Series Champion Boston Red Sox have hit 25 batters in 39 games, putting them on pace to drill 103.8 batters this year. The all time record is held by the 1899 Cleveland Spiders with 109. If the Red Sox put up 103 that will rank second, ahead of the 1899 New York Giants who hit 100. Third on the list, and the modern record holder, are the 2003 Tampa Bay Devil Rays who plunked 95 batters, just beating their 2002 record of 94 plunks.