None of those units that benefit from cover saves are in a situation where more than half the unit is not in cover, hence why they do not invalidate the situation with the KFF nor do they provide a precedent by which it can reasonably follow.
Lictors - more than 50% of the unit is in cover no matter what, what need is there of a clarification? Same for warbikes, etc.
In this situation, you have an area of effect within which lies a cover save. In the absence of some special rule granting a unit with even one model inside, and such rule does not exist, you naturally follow both the precedent and the standard for cover saves. It's a no-brainer.
Cover applies to units. Determining cover applies to model count. The KFF refers to units, and so does cover. I.E. if your UNIT is within a section of trees, you get a 5+ cover save. Similarly, if your UNIT is within 6" of a KFF, you get a 5+ cover save. When then determining WHETHER the aforementioned unit is within cover, you refer to a special rule where one exists (i.e. Lictors are always in cover) or the general rule for determining it where one does not exist (KFF). This is to say that, quite clearly, Lictors have a rule that says no matter what they get "xyz" cover save. This overrides any kind of question mark - is it a Lictor? Cool, it gets a cover save, and the special rule goes on to tell you what that save will be. The KFF does not state a special rule excepting the normal requirements for acquiring a cover save where one exists - in this case, within 6" of the big mek - and so you must follow the rules in place. You cannot create a new rule where one is not written, which is EXACTLY what must be done to claim that having ANY % of a model w/in 6" counts as gaining a cover save from a KFF.
If we are in the business where you can willy nilly invent addendums to rules to sway them in your favor away from the precedent and standards of the game, count me out of 40k. The writing is bad enough already without that liberality being added.
Trying to claim that the wording is different is a semantics game, but one that is unnecessary here. The wording for trees or any other cover is identical to KFF - unit within. When determining IF a unit is "within" you then use the rule using model count. It's pretty clear regardless of the way you word it.
Precedent can further be extended using rules for similar abilities across other armies, if you feel like using precedent instead of RAW (which support majority w/in 6"). Necron Res Orb specifically states if ANY portion of a unit, rather than "unit within." The same applies to various other abilities throughout. All of that, however, is irrelevant. One cannot use the Objectives standard from take and hold (where the entire unit must be within) b/c it is an objective, not a cover save. One cannot use the res orb standard, b/c that is not a cover save. EVEN if you refuse to believe that this cover save isn't cover (I mean, really?), the best you can do is then revert to nearest precedent. That nearest precedent is - you guessed it - the rules for cover! Again, the definition and explanation is clear. The KFF causes an area of the board to grant a cover save. Looks like cover, sounds like cover, has no special label saying oh wait but it isn't, it gives any unit with even one model ... cover.