Q - "When is a Carrick NOT a Carrick?"
For me, this question teeters dangerously close to :-
"The King has no cloths" or perhaps "Struth cobba, Ashleys forgotten his strides"
It seems to me that 'just about' anything that can be arranged in a carrick-esque style is being classified as a variant of the Carrick. From where I am standing, that is just plain wrong and I am keen to hear other opinions on the subject.
For me, the Carrick is unique. It is the knot Dave Root depicts in his knotting Index as the Carrick Bend or ABOK#1439
http://www.layhands.com/knots/Knots_Bends.htm#CarrickBend and it is the intermediary knot formed in the first few folds of Willekes method of making the Chinese Button knot. It is a closed four strand plait. It has an Overs Index of 8 and is fully saturated with 16 reversals (i.e. it is an 8:16)
Let me make my point with an example which hopefully everyone agrees with.
Take a piece of cord and lay it down in three overlapping loops to create the shape of the Carrick like this :-

It has the double end loop shape and the central diamond. It has an Overs Index of 8 (but it has a saturation of 6). It looks like the Carrick, but I hope everyone agrees that this is nothing more than a pile of cord. If you rationalise it to its simplest form it reduces to just a straight piece of cord i.e 0:0 So just because it 'looked' like a Carrick, it did not mean that is was the Carrick - Agreed?
Going a little further, instead of simply laying the end on the pile, pass it - under, over and under the last three strands that it would have crossed over in the previous example.

It still looks like the Carrick shape. It still has an Overs index of 8 and complexity has shot up to 13. But is it a Carrick? Rationalise it and it reduces to the Overhand knot (3:6). So was that a Carrick? I would argue that it most definitely is not a Carrick. What it is, is an overhand knot plus a pile of string - Agreed?
Now lets step into the 'dirty water'. Either make the following shape, or tie the Granny knot and reform it to this shape.

This knot looks like the Carrick, has an Overs Index of 8 (but still only has a complexity of 8, i.e. 8:8 ). When the knot is rationalised it returns to the Granny with its classification of 6:12. So why is this knot, which is no more than two overhand knots, now grouped in with the Carrick 'family'? Surely this is simply the Granny - with a pile of string!
For me, this, and other 'sub Carricks' are not Carricks at all and should not be classified as such. For me, the Carrick is not only its shape, but more importantly, it is its complete saturation.
Dare I say it! I think Ashley is wrong and there is only one Carrick and that is the full 8:16
Q - "When is a Carrick NOT a Carrick?" A - "When it's a pile of string"