Actually, under Fed, NCAA, and OBR, the strikeout would be credited to the relief pitcher in the situation mentioned above. In fact, so would a BB had the batter been walked. The previous pitcher would have been charged with a walk if the reliever had inherited a 2-1 or 2-0 count, but not 2-2.
The OBR rule is currently 10.16(h) [it used to be 10.18(h)]. NCAA is 10.22b. Fed is 9-6-5.
Fed:
9-6-5
A relief pitcher shall not be charged with any earned run scored by a runner who was on base when such pitcher entered, nor with any hit or advance by a batter who had more balls than strikes when such pitcher entered.
NCAA:
10.22b
...if a batter has more balls than strikes, unless the count is one ball, no strikes, when a relief pitcher enters the game and the batter receives a base on balls, charge that action to the preceding pitcher. Any other action of the batter shall be charged to the relief pitcher.
OBR:
10.16
(h) A relief pitcher shall not be held accountable when the first batter to whom he pitches reaches first base on four called balls if such batter has a decided advantage in the ball and strike count when pitchers are changed.
(1) If, when pitchers are changed, the count is
2 balls, no strike,
2 balls, 1 strike,
3 balls, no strike,
3 balls, 1 strike,
3 balls, 2 strikes,
and the batter gets a base on balls, the official scorer shall charge that batter and the base on balls to the preceding pitcher, not to the relief pitcher.
(2) Any other action by such batter, such as reaching base on a hit, an error, a fielder's choice, a force-out, or being touched by a pitched ball, shall cause such a batter to be charged to the relief pitcher.
Rule 10.16(h) Comment: The provisions of Rule 10.16(h)(2) shall not be construed as affecting or conflicting with the provisions of Rule 10.16(g).
(3) If, when pitchers are changed, the count is
2 balls, 2 strikes,
1 ball, 2 strikes,
1 ball, 1 strike,
1 ball, no strike,
no ball, 2 strikes,
no ball, 1 strike,
the official scorer shall charge that batter and the actions of that batter to the relief pitcher.