I have eaten them. But I know some more-kosher-than-thou types who won't partake. Those are the Jewish folk who answer to an even "higher authority" than Hebrew National.
Kenneth Lasson, writing in a Baltimore Jewish Times cover story in 2009, weaves together reportage about the hot dog industry, the kashrut supervision industry and baseball parks to come up with a fascinating fabric of a story, "Hebrew National and Kosher Politics - What’s kosher about answering to a higher authority?".
For years there have been some super-glatt-orthodox who whisper about whether the supervision of Hebrew National was "reliable." Lasson covers this controversy and says for instance,
...As to Triangle K, Rabbi Abadi wrote on the kashrut.org Web site, “Rabbi Ralbag is a G-d-fearing man and if he says it’s kosher, you sure can eat it. I can’t say the same for many of the other labels out there.”...more...The Talmudic question is of course, can we trust the writing of Kenneth Lasson. Is he reliable? Is he glatt kosher? /repost from 7-9-09/