The second part of the definition of keep clear answers your question:

A boat keeps clear of a right-of-way boat
(b) when the boats are overlapped, if the right-of-way boat can also change course in both directions without immediately making contact.

Bearing away is one of the directions for changing course.  If there was immediate contact then the windward boat was not keeping clear.  If the course change by the leeward boat is more substantial, i.e. a "hard luff", then the leeward boat is not giving the keep clear windward boat the room it needs to continue keeping clear after the course change.

There is no specific amount of room, e.g. 1 meter, 10 cm, 1 foot, that defines how close is too close.  This is one of those times where the standard judging answer of "it depends" applies.  It depends on the seas state, the wind, the types of boats, and any other conditions that effect how the boats move and how much control they have.  But if the windward boat is at all concerned about how close they are to the leeward boat then they are probably too close.  You have to give more space in 3m waves than 1cm waves.

'It depends' also depends on how the leeward boat came to be in that position. If it put itself in a position where it was impossible to change direction without contact, then Rule 15 applies. If the overlap had been established for some time, let's say 5+ seconds in a dinghy, and 15 did not apply, then the windward boat should have started to increase the distance between the boats. Which is not to say that there is a 5 second cut off for 15, but that the windward boat should make some attempt to increase the distance within a reasonably short time. As John says, boat size and racing conditions need to be taken into consideration.

In the US, we used to have an Appeal between Navy 44’s which illustrated this point well, but it’s been retired.

We still have US Appeal 119 which combines 15 and 16 into a single scenario.   As you can see, there is a dance between the boats and you have to watch the feet and see who is stepping the other’s toes :-)

PS:  As you can see in the appeal, it often is highly dependent upon the orientation of the boats bow to stern.  For instance. …

A leeward boat (L) bow forward of a windward boat (W) on a beat with W's bow amidship of L .. if L luffs to windward, L's stern moves away from W and W's stern is clear to rotate without contact. 

Flip that geometry, W is bow-out on L … when L turns to windward she is narrowing the space between her bow and windwards stern.  W can’t turn to windward because her stern would hit L's bow, therefore she is too close for L to turn in the windward direction.

In the 2nd scenario, if W had fallen-down into L in this position, W needs to keep a little more room understanding that L's bow and her stern movement add to each other to reduce room to maneuver. 

Even if the boats are gunwale to gunwale (meaning windward has already failed to keep clear) windward would still have the option to keep clear without making contact by maintaining course, easing sheets and slowing down.

Tim, if the windward boat eased its sheets, the sheets, sail and/or boom would likely hit part of the leeward boat: their deck, crew, shrouds, or lifelines. So, no, what you're proposing is not an option for windward to keep clear in most situations.