Rather like conflating the Tamil Tigers and the Lions Club.
That is hilarious.
I know humor is underappreciated here, but that deserves a million upvotes.
I cannot speak for what process the DHS or the TSA use, but what is done in the industry to ensure the person they're transacting with is not on some blacklist (which is mandatory, as per OFAC regulations) is using fuzzy string matching algorithms. Usually it's some variant of measures like the Jaro-Winkler distance [1], which is commonly used to compare names, or phonetic algorithms like Soundex [2], which we know is used by the US government for the census.
Unfortunately, these algorithms tend to work reasonably well for western names but not so much for picking up the subtleties of other languages and cultures, like "islah" (which apparently means "reform") vs. "islam". It wouldn't surprise me if the the DHS simply relies on automatic discovery algorithms and does not have a team of sufficiently trained people with both the language skills on call to do manual checks.
[1] http://en.wikipedia.org/wiki/Jaro%E2%80%93Winkler_distance [2] http://en.wikipedia.org/wiki/Soundex
It doesn't explain the subsequent incident where the government (apparently) placed her daughter on the no-fly list as well, and then went on to (apparently) lie about it in court.
There is no excuse to the government allegedly lying in court, but I have a hard time imagining anyone would do such a stupid move in their right mind. What could one hope to achieve by putting the daughter on the no-fly-list in the first place? That the key witness missing her flight would cause her testimony to be ignored? That stalling the process by a few days would tip the balance in their favor? That the consequences of the plot being discovered (which depended on the Malaysian airline keeping its mouth shut) do not considerably outweigh its benefits? Also noteworthy is that this particular case is an appeal to a first decision back in in February 2012 that the DHS won, for reasons completely unrelated to Dr. Ibrahim being or not being able to board the flight: http://caselaw.findlaw.com/us-9th-circuit/1438741.html