How does a fumble at kickoff or a punt - recovered by kicking team - affect win conditions in overtime?

Question

In the NFL, Overtime conditions state that if the team to possess the ball first score a Touchdown on their first possession, then they win the game. If they score a Field Goal, or fail to score, then the other team has a chance to possess the ball.

Now let's look at the following examples:

Team A has won the toss in overtime and has elected to receive the kickoff. Team B kicks the ball and it is returned by Team A. During the return, the runner fumbles the ball and it is recovered by a member of Team B.

Does Team B need to score a Touchdown or a Field Goal to win the game? As they are the first team to run a down.

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Similarly...

It is 4th down for Team A, on the first possession of overtime, and they decide to Punt. Team A punts the ball down the field. A fair-catch is called, but the returner from Team B does not cleanly collect the ball, and muffs it. It is then recovered by Team A.

Does Team A still need to score a Touchdown to win the game, or do they now only require a Field Goal?

Answer 1

In both scenarios only a Field Goal is required to win the game. This is because it is deemed that the receiving team in both instances has had their opportunity to possess the ball.

From the 2019 NFL Rulebook: Rule 16 - Section 1 - Article 3

Article 3. Extra Period

[...]

(e) The opportunity to possess applies only during kicking plays. A kickoff is the opportunity to possess for the receiving team. If the kicking team legally recovers the kick, the receiving team is considered to have had its opportunity. A punt or field goal attempt that crosses the line of scrimmage and is muffed by the receiving team is considered to be an opportunity to possess for the receiving team. Normal touching rules by the kicking team apply.