|Mort the Cleverly Named|
It is directly below the linked FAQ:
For example, the Dimensional Agility feat (Ultimate Combat) has "ability to use the abundant step class feature or cast dimension door" as a prerequisite; a barghest has dimension door as a spell-like ability, so the barghest meets the "able to cast dimension door prerequisite for that feat.
Edit 7/12/13: The design team is aware that the above answer means that certain races can gain access to some spellcaster prestige classes earlier than the default minimum (character level 6). Given that prestige classes are usually a sub-optimal character choice (especially for spellcasters), the design team is allowing this FAQ ruling for prestige classes. If there is in-play evidence that this ruling is creating characters that are too powerful, the design team may revisit whether or not to allow spell-like abilities to count for prestige class requirements.
Personally, I've actually found it to be pretty great. Dumpster diving for the correct spell levels is annoying, and I agree it is a VERY weird interpretation, but it has made Eldritch Knight a much more viable option (as well as Mystic Theurge, though that might be a bit TOO attractive). I'm made some neat, balanced characters with it that otherwise just wouldn't have worked.
Haven't seen the new class yet, but from what I'm hearing it won't be a game breaker there either, even if it was an unintended option.