Jihad is wrong, sickles. The definition you mention as "extremist" is, in fact, the generally-accepted definition of jihad throughout Islamic thought and history.
It's a minority who subscribe to the "peaceful" definition of jihad. They're trying to "reclaim" the term, by redefining it with a meaning never suggested until the 19th century. Frankly, they might as well try to reclaim "lebensraum."
Tacitus is wrong.
Muhammad SAW never fought an offensive war. The abuse of the term jihad did start with the Caliphs 1 - 3, and was restored to its rightful meaning and implementation under Ali ibn Talib AS (4th Caliph and the true Imam of the Shi'a).
Religious concepts are not as mutable as linguistic words. They are absolutes. Tomorrow if the word "baptize" were to gain widespread acceptance as slang for "fornicate", it would be no less irrelevant to the actual meaning of the concept. As long as a sole Catholic remained performing baptism in the true sense, the truth of the word would be eternal.
But Tacitus is wrong to argue that the majority of the world's muslims believe that jihad means an offensive war waged against innocents (ie, hirabah). The majority of the world's muslims do not engage in violence and respond to Bin Laden's amply-broadcast and distributed calls to hirabah via satellite television and the internet. The Arab street did not rise. The Holocaust - a large-scale, systematic genocide of a specific religious group - has not been repeated in history. If Tacitus was right, the world would be a blood bath on a scale as you can not imagine - just look at the Hajj and imagine that sole dedication of purpose turned towards a violent end.
And Tacitus is even wrong to assert that to moderate muslims like myself, jihad has a purely peaceful definition. In fact jihad does permit violence - in defensive measures. The best analogy to this aspect of jihad is "Jacksonian" warfare - don't start war, but when attacked, win. Then show mercy and make sure your enemy sees the wisdom in being your friend. If they don't get it, though, educate them on what it means to be your enemy.
This is the lesser jihad. A greater jihad is that of the tounge, whereby you speak out against evil and defend yourself and the faith through argument.
The greatest jihad, however, is that of pious action - by simply living in accordance with Islamic teachings. In so doing, you act as an example of the faith to others. This jihad is the greatest jihad because it is also the most difficult.
All of these aspects of jihad were elucidated by the Prophet SAW, are described in the Qur'an, and were further explained by Ali AS. This definition of jihad therefore dates from the 7th century, not the 19th.
Compendiums of false hadith such as the complete works of Bukhari are the only source of hadith that are used to justify hirabah. Bill Allison provides some excerpts from Farid Esack's The Qur'an: A Short Introduction, that describes the hadith manufacturing industry in detail:
With Sunnah now equated with the sunnah of Muhammad and elevated to the level of a source of religio-legal authority, and with Hadith established as the only means to authenticate Sunnah, the various disputants attempted to justify their views and to strip their opponents of legitimacy on the basis of Hadith. This contributed to the emergence of both a corpus of Hadith literature and an entire science around it, much of it based on the growing informal hadith manufacturing industry.
Brown notes that the "extent of the forgery was dramatic. Forgers became active even during the life of Muhammad, in spite of the warning that whoever spreads lies about him would burn in hell. In the Caliphate of 'Umar, the problem became so serious that he prohibited transmission of hadith altogether. Forgery only increased under the Umayyads, the first dynasty of Islam that reigned from 661 until 750. They considered hadith a means of propping up their rule and actively circulated traditions against 'Ali in favor of Mu'awiyah [ibn Abi Sufyan (d. 680), the founder of the dynasty]. The Abbasids [who succeeded them] followed the same pattern, circulating Prophetic hadith which predicted the reign of each successive ruler. Moreover, religious and ethnic conflicts further contributed to the forgery of hadith. The Zanadiqah (those who professed Islam while holding Manichean ideas, as we are told by the heresiographers), for example, are reported to have circulated 12,000 fabricated traditions. The degree of the problem can be seen from the testimony of the muhaddithum themselves. Bukhari, for example, selected 9,000 traditions out of 700,000."
A majority of muslims do indeed honor Bukhari as legitimate, but still do not rise in jihad against their non-muslim neighbors. It is only a small subset indeed that take the false hadith and twist them further into their contorted arguments.
The greatest jihad has been waged every day by the vast majority of muslims in their daily lives, which far outstrips the hirabah of the terrorists and despots, who would try to invoke it to lend their political causes false legitimacy.
 Dan pulls no punches and demonstrates how the Saudis have largely been doing nothing, and how even right now noted financiers of Al-Qaeda remain free. But that there has been a shift in the Saudi royals' thinking, there can be little doubt. Whether the Saudis make a different cost-benefit calculation remains to be seen.