The Online Etymology Dictionary entry for the word fee might help:
...The other word is Anglo-French fee, from Old French fieu, a variant of fief "possession, holding, domain; feudal duties, payment" (see fief), which apparently is a Germanic compound in which the first element is cognate with Old English feoh.
Via Anglo-French come the legal senses "estate in land or tenements held on condition of feudal homage; land, property, possession" (c. 1300). Hence fee-simple (late 14c.) "absolute ownership," as opposed to fee-tail (early 15c.) "entailed ownership," inheritance limited to some particular class of heirs (second element from Old French taillir "to cut, to limit").
The feudal sense was extended from landholdings to inheritable offices of service to a feudal lord (late 14c.; in Anglo-French late 13c.), for example forester of fe "a forester by heritable right." As these often were offices of profit, the word came to be used for "remuneration for service in office" (late 14c.), hence, "payment for (any kind of) work or services" (late 14c.). From late 14c. as "a sum paid for a privilege" (originally admission to a guild); early 15c. as "money payment or charge exacted for a license, etc."
So given the word usage in the mid-12th century I would say yes, it could be like a knight's fee. Or it could be the 'heritable position'
Using a totally different source (not related to the profile) to illustrate usage in terms of property: Edward Miller's The Abbey and Bishopric of Ely contains this:
"The actual deed in question may have survived - a charter in which Prior William granted Eye and Coveney to Eustace, the bishop's butler for the service of half a knight. Both may have been resumed into demesne in 1135; and though Eye returned to the butler's fee, Coveney must at some time or another have been given to the convent...."