Hillis, D.H. (1999) SINEs of the perfect character. Proc. Natl. Acad. Sci. USA 96: 9979â9981.
Not the latest paper on the subject. There's one "LINEs of an almost perfect character"... I'll try to look some of them up after the SVP meeting (I leave this evening, because the field trip to the fissure localities starts tomorrow at 8 am).
In short: yes, SINE and LINE insertions can happen convergently, and precise excisions can also happen; it's just extremely improbable.