This illustrates how the same object is treated differently based upon circumstances. How about a batted ball that strikes a bat in fair or foul territory?

NFHS's rule for an on-deck batter mirrors the blocked ball rule. In both of OP's scenarios, how would you rule if the person hit on the field was the in-the-hole batter, a bench player not currently in the game, the batgirl, or a ball-shagger?

In OP's second scenario, the defense is at fault. In the first, the offense is at fault. Similar actions, same object, different subtleties. Applying a black and white rule to gray areas will create perceived injustices.

USA Softball clarification
 

Play: With R1 on 3B and R2 on 2B and 1 out, B4 hits a fly ball to F7. Both runners tag up and attempt to advance after the catch. The on-deck batter leaves her bat in the on-deck circle on the first base side of the field to direct the runner(s) coming home. F1 has taken a position behind the on-deck batter, third base line extended, to back up the throw.

In a) F7 overthrows F2 in an attempt to retire R1 and the thrown ball deflects off the on-deck batter's helmet and goes out of play; in b) the overthrow hits the on-deck batter and deflects away up the first base line and as a result, R2 now attempts to score but the deflection has eluded F1 backing up the play; in c) the overthrow ricochets off the fence and hits the on-deck batter's discarded bat in the on-deck circle.

Ruling: a) This is a blocked ball. The ball all is dead, each runner is awarded 1 base at the time the ball became blocked, Rule 1 Definitions. and Rule 8-5G Exception 1
b) Same as a
c) Ball is blocked due to offensive equipment not in the game; ball is dead, runners return to last base touched at time of block and if the block prevented the defense from making an out the runner being played on is out. Rule 8, Section 5G Exception 3 and Effect.

As far as I know, it is a blocked ball, as defined in 2-2-3. Rule 5-1-1g applies to it being dead and runners as Ted posted:
"Effect:
a. The ball is dead.
b. Runners are returned to the last base touched at the time of the blocked
ball.
c. If the blocked ball prevented the defense from making an out, the runner
being played on is out."

BTW, fault is not the issue.

None.