If a boat establishes an overlap from clear astern, it is by definition traveling faster than the other boat. I would conclude that it is act of overtaking that established the overlap. 
My reading of the rule is that if the overtaking boat established the overlap to leeward, she must give windward opportunity to respond. 
If the same boat established an overlap to windward from clear astern, I would say that the leeward boat acquired ROW via the action of the other boat overtaking and therefore can luff to protect her wind. The overtaking boat from clear astern. 
Of course, there is still the requirement to avoid collision. 

As Anthony has stated, if the overtaking boat establishes a leeward overlap, she is bound by R15 to initially give the windward boat room to keep clear.  However, if the overtaking boat establishes an overlap so close to windward that she is unable to initially keep clear, then it is on her and she has no protection from R15.  If leeward then luffs, leeward is obligated under R16.1 to give windward room to keep clear.  
Murray

The 'action' in the case described in the OP is the establishment of the leeward overlap where the ROW changes and rule 15 applies.  The boat clear astern could have slowed down to prevent the overlap or gone to windward and thus not gained the ROW.  The ROW clearly changes from one boat to the other when the leeward overlap is created.

Anthony - if the boat originally clear astern establishes an overlap to windward of the boat originally clear ahead, the ROW has not changed and thus rule 15 does not apply.

Rule 16 will always apply regardless of whether rule 15 applies.

Good point, John. Clear ahead was ROW and remains ROW when it becomes overlapped to leeward (due to the actions of the previously clear astern boat). 
Clear ahead was free to come up prior to the overlap and remains so. 
While the identity of the ROW boat has not changed in that case, it is a new situation. 
I'm trying to think of a situation where the identity of the ROW boat doesn't change, but situation is different and might require a boat to limit the timing of a course change. Every one I can think of would involve a course change by the ROW boat, and there fore rule 16 would put some constraints on the ROW boat. 

How about rule 17 ?
when overlaps on leeward ?

I can't see how sailing fast is an act, whilst sailing slow is not.  For example, what if the slow boat is doing a sail change, so surely it would be their action that caused them to sail slow.

I key is that the rule is written with a negative exception: when acquiring rights, you must initially give room UNLESS gained rights by the other boats action.   So it the example of a boat gaining an overlap from behind, the default situation is that they must initially give room UNLESS there was a specific action of the other boat that caused the overlap.    So it is not that a boat acted to gain an overlap, it is that the other boat didn't act to give it. 

"Overtaking" is an act recognized in COLREGS and our inland water regulations as well. In fact, it is the only time where a sailboat always gives ROW to a recreational motor boat (even if not in waterway where the powerboat has limited maneuverability).  I don't see any problem with applying it here. Though your point about the way it is phrased is a valid one. 

I think Greg is right.  Sailing faster or slower is not, without more, an 'act' or 'action'.

Match Race Call B18

Rule 11; On the Same Tack, OverlappedRule 12; On the Same Tack, Not OverlappedRule 15; Acquiring Right of Way

An increase or decrease in speed is not in itself an 'action' within the meaning of the second part of rule 15. 

A few posters here have been on a wild goose chase for meanings of terms that are not in the RRS.

A boat does not 'establish an overlap'.  Boats 'become overlapped'.  The 'establishes' language was removed from the RRS in the 1995 rewrite to avoid just this sort of argument.

'Overtaking' is not a word used in the RRS.

I can't recall seeing the words 'wild' or 'goose' used in the RRS either.  Yet all these words have meanings ordinarily understood in nautical or general use.