Detailed Explanation
My Skin or My Kin? invokes the following laws:
1. If A notices an overflowing river nearing his field, he may divert the water even if by doing so, the water will overflow towards B's field.
2. Once the water has entered A's field, A may not divert the flow into B's field [Yerushalmi Bava Kama 3: 1].
3. The duke decreed that two of the townspeople should be taxed. Each townsperson may individually try to absolve him/herself from the tax, knowing that someone else will probably end up having to foot the bill.
4. Once the duke chooses A to pay the tax; A may NOT persuade the duke to absolve him/her from the tax, knowing that someone else will have to pay in his/her stead [Choshen Mishpat 163, Sh"ach 18].
5. False accusations were directed at A. A may not deflect them if B will automatically be incriminated.
6. However, if B is in fact the culprit, while A may not say that B is guilty, he/she is permitted to say, "it was not me" [Sefer Chofetz Chaim: Hilchos Lashon Hara chapter 10, Be'er Mayim Chayim 43/ Note: See ibid. Righteous people will often take the blame anyway.].
7. It is forbidden to hand a fellow Jew over to the enemy, even in order to save other lives. [Rambam Hilchos Yesodei Hatorah 5: 5 See also, Sefer Alei Meroros from Rav Yehoshua Moshe Aharonson 1996].
Application:
If Yonatan was deserving of reprimand, Yair does not need to take the blame. He may not say that Yonatan cut the curtain but may say that he did not.
The Council may not hand over their brethren. The same dilemma was posed in July 1942. Rav Aharonson ruled that the council should abstain and so they did.
Avi was selected. As Avi's brethren are not deserving of such treatment, Avi may not save his skin by means of causing another to be put on death row