DH rule error in game?

Was reading my game recap and I think this may be an error:

http://onlinegames.strat-o-matic.com/game/223460/656

The DH, Murray, was hurt. HAL brought in someone to take his spot in the lineup, but put him in RF. He then pulled the PR he had for the LF and put in McCracken at DH there. As far as I know, moving the DH spot is never a possibility. If I'm wrong, I'd like to know. If I'm right, well, it should probably be addressed.

Nothing wrong with that substitution. You can move the DH around anywhere you want.

Looks like a legit move to me.

What you can not do is take a player out fo the DH spot and put him in the field.
Murray was PH for so it was legal. Think of it as a double switch.
It would have been illegal to move Murray from DH to 1B.
I believe in a circumstance like that, you would be forced to forfeit the DH and the pitcher would have to hit for the remainder of the game.

Here's the rule from the MLB website. The DH has to stay in the same spot in the order (i.e. the player put in RF should have been the DH). So, I do think there was an issue with the DH use in the game.

6.10
Any League may elect to use the Designated Hitter Rule.
(a) In the event of inter-league competition between clubs of Leagues using the Designated Hitter Rule and clubs of Leagues not using the Designated Hitter Rule, the rule will be used as follows:
1. In World Series or exhibition games, the rule will be used or not used as is the practice of the home team.
2. In All-Star games, the rule will only be used if both teams and both Leagues so agree.
(b) The Rule provides as follows:
A hitter may be designated to bat for the starting pitcher and allsubsequent pitchers in any game without otherwise affecting the status of the pitcher(s) in the game. A Designated Hitter for the pitcher must be selected prior to the game and must be includedin the lineup cards presented to the Umpire in Chief.
The designated hitter named in the starting lineup must come to bat at least one time, unless the opposing club changes pitchers.
It is not mandatory that a club designate a hitter for the pitcher, but failure to do so prior to the game precludes the use of a Designated Hitter for that game.
Pinch hitters for a Designated Hitter may be used. Any substitute hitter for a Designated Hitter becomes the Designated Hitter. A replaced Designated Hitter shall not re-enter the game in any capacity.
The Designated Hitter may be used defensively, continuing to bat in the same position in the batting order, but the pitcher must then bat in the place of the substituted defensive player, unless more than one substitution is made, and the manager then must designate their spots in the batting order.
A runner may be substituted for the Designated Hitter and the runner assumes the role of Designated Hitter. A Designated Hitter may not pinch run.
A Designated Hitter is “locked” into the batting order. No multiple substitutions may be made that will alter the batting rotation of the Designated Hitter.
Once the game pitcher is switched from the mound to a defensive position this move shall terminate the Designated Hitter role for the remainder of the game.
Once a pinch hitter bats for any player in the batting order and then enters the game to pitch, this move shall terminate the Designated Hitter role for the remainder of the game.
Once the game pitcher bats for the Designated Hitter this move shall terminate the Designated Hitter role for the remainder of the game. (The game pitcher may only pinch-hit for the Designated Hitter.)
Once a Designated Hitter assumes a defensive position this move shall terminate the Designated Hitter role for the remainder of the game. A substitute for the Designated Hitter need not be announced until it is the Designated Hitter’s turn to bat.

I see 2 contradictory statements in that rule.

"The Designated Hitter may be used defensively, continuing to bat in the same position in the batting order, but the pitcher must then bat in the place of the substituted defensive player, unless more than one substitution is made, and the manager then must designate their spots in the batting order."

and

"A Designated Hitter is “locked” into the batting order. No multiple substitutions may be made that will alter the batting rotation of the Designated Hitter."

Unless I'm misunderstanding one of those rules. They seem to contradict. One rule says you can double switch the DH spot with another spot in the order, and another rule says you cant.

"The Designated Hitter may be used defensively, continuing to bat in the same position in the batting order, but the pitcher must then bat in the place of the substituted defensive player, unless more than one substitution is made, and the manager then must designate their spots in the batting order."

The relevant part to me is here . . . "but the pitcher must then bat in the place of the substituted defensive player, unless more than one substitution is made" . . . this means the pitcher could bat in another spot, if the manager made a double switch. Not that the DH can swap around, if you follow the other rule you quoted.