Assuming that both the information in the AQAP Statement and the information in the 26th of September is correct, then it seems that al-'Ujayri originally came from the al-Jarrah clan, which is from the village of al-Barh in Taizz (see mu'ajam al-buldan wa al-qaba'il al-yamaniyya Vol. 1 pg. 306). The kunya he selected, Abu 'Ubaydah, and his name al-Jarrah, then, is ironic as this is also the name of an early companion of the prophet, Abu 'Ubaydah al-Jarrah, who is a widely respected figure in early Islamic history.
The irony comes in when one digs a bit further. In the current issue of Sada al-Malahim, one of the fatawa published deals with whether or not Yemen is a part of the Arabian Peninsula. This is important as AQAP relies on the hadith that states: "expel the infidels from the Arabian Peninsula," so if Yemen is part of the Arabian Peninsula, then the AQAP's attacks against infidels have religious justification, at least in the organization's own eyes. The fatwa in Sada al-Malahim is lifted from the writings of someone the magazine identifies as Shaykh 'Abdullah Nasir al-Rashid (thanks to Thomas Hegghammer I have been able to identify him as the pen name of 'Abd al-Aziz al-Anzi, who wrote for Sawt al-Jihad and was arrested in 2006 and is currently in a Saudi prison). In some of al-Rashid's writings, which are available here, he actually attacks a version of the hadith about expelling the infidels that was transmitted by Abu 'Ubaydah al-Jarrah as weak.
So in the end, one has a suicide bomber named Abu 'Ubaydah al-Jarrah carrying out an attack on the basis of a hadith that is significantly different from the one his early Islamic namesake transmitted. Of course if one accepted the hadith transmitted by the original Abu 'Ubaydah al-Jarrah then AQAP would have no religious justification for its attacks, or at the very least would have to articulate a new reason, but their current justification would not hold.