Those 2 guys did blow 13 save opportunities out of 24, but here is why that stat is misleading.
BR defines 'save opportunities' as simply saves + blown saves. So yes, the times a reliever pitches the 8th and blows the save is counted as a save opportunity. Pitchers that often pitch in the 8th inning or earlier are getting penalized for blown saves, but are not getting any credit for any of the successful holds.
Let's say that Barnes comes into the 8th inning in 20 games and successfully holds 15 of them. That's a success rate of 75%, with 5 blown saves.
Then he comes into a save situation in the 9th inning in 5 games and successfully saves all of them. That's a success rate of 100%, with 5 saves.
Between the 8th and 9th innings, Barnes was successful 20 out of 25 times, or 80% of the time.
With BR's definition of save opportunities, Barnes had 10 save opportunities, and was successful in only 5 of them, making his success rate only 50%. All of his successful holds are ignored with that stat.