Around the time of his death al-Aqsa was seeking to cut links with Arafat[2].
To claim that Sharon was trying to cut any kind of deal with the Palestinians is... unusual. (For those not aware, it was former Israeli PM Aiel Sharon's visit to the Moslem area of Temple Mount in Jerusalem that sparked the second intifāḍah[3] (prior to him becoming PM). The al-Aqsa Martyrs Brigade is named after this incident).
Additionally, Arafat's Fatah group was seen as the one group strong enough to keep Hamas controlled.
The al-Aqsa Martyrs Brigade was a problem for Israel, but it was seen as much less of a problem than Hamas. Subsequent events would show this view was probably correct: When Abbas took control of Fatah it quickly lost control of Gaza to Hamas, and the Israelis have consistently struggled to find a successful approach to dealing with Hamas in Gaza (eg, they later fought a fairly unsuccessful war to try to control Hamas in Gaza).
Edit: Although I disagree with you, I think you do make some good points. You were downvoted when I wrote this, so I have upvoted you.
[1] http://books.google.com.au/books?id=CGiot772MSEC&pg=PA77&dq=...
[2] http://www.worldtribune.com/worldtribune/WTARC/2004/me_pales...
[3] http://www.britannica.com/EBchecked/topic/538892/Ariel-Sharo...