The article discussed the vowel problem with the band "Eagles", a band that doesn't have a name prefixed by a definite article. However, we often apply one in use - even the band does. That's evidenced by their album covers. Where the band name leads the titling, there is no "The" - it's only when additional text is included that "THE" gets added (a capped "The" being appropriate for title format). So you get confusion:
EAGLES - THEIR GREATEST HITS 1971-1975
THE VERY BEST OF THE EAGLES
This is confusing enough that the wikipage for the band actually appeared as part of a question sequence on Only Connect. I can't remember the other three clues involved, but the lateral link was that all of them were pages frequently contested on Wikipedia. Eagles was clued as:
Currently, the wikipage seems to use the name correctly applying a definite article before the name at the start of a paragraph ("The Eagles are . . .") while using "Eagles (band)" as a header. "The Eagles" searched redirects to the "the-less" page. It's a reasonable compromise.