Indeed. The Din that a ba'al writes a get is more than a peirush mekubal, it's an ofener passuk.
dont know what "ofener" means, but the simple read is not at all clear, as i have noted earlier. All the torah says (and indeed a simple read could be,and perhaps the mesorah read of the simple text ) is that if u hate your wife, u have a mitzvah to write out a bill of divorce stating the separation details (u get back this, i give u this etc.), and send her away. Indeed, the offhand reference to this mitzvah in the middle of psukim clearly focused on the issur (and toevah) of getting back together with a women who swapped for another man (note all the descriptive "ve"s in the pasuk,
http://www.mechon-mamre.org/p/pt/pt0524.htm, if vekasav lah is a necessary component for a good get (as opposed to a component for this toevah of remarriage), is it also necessary for a get that the women actually marries another man?) points to there not being an absolute Torah-pshat-level requirement that a woman cannot go marry someone else if the guy throws her out/they agree their marriage is over.