Replay Review / Double Play!?

[cmcramer]

Much discussion about this play among our group of baseball fans here; your expertise is appreciated!

MLB rules. No outs; R1

Second baseman short-hops or maybe catches a low, sinking line drive as he dives to his right. He gets up, holds glove/ball up high, looking at the Ump. Ump signals SAFE, so second baseman decides to take a sure out and throws to first base as runner - who was running on the pitch - advances to second base.

Upon review, ball WAS A CATCH! Does the runner go back to first with one out, or is this a double play. Even after reading the relevant rules....it seems like it could go either way!

IV. Correcting an Incorrect Call
Consistent with Official Baseball Rule 8.02(c) (formerly Rule 9.02(c)), if Replay Review results in a change to a call that had been made on the field, the Replay Official, to the extent feasible, shall exercise his discretion to place both Clubs in the same position they would have been in had the call on the field been correct.This shall include placing runners where he thinks those runners would have been at the conclusion of the reviewed play if the reviewed call had been correctly made in the first instance, disregarding interference or obstruction that may have occurred on the play, failures of runners to tag up based upon the initial call on the field, runners passing other runners, missing bases, etc.
A. Placement of Runners.
1. Replay Official's Responsibility. All decisions regarding the placement of base runners resulting from a call that is overturned pursuant to these Regulations shall be made by the Replay Official in accordance with the standard set forth in the Official Baseball Rules.
2. Book Awards & Discretion. Unless directed otherwise by the Official Baseball Rules (for example, Official Baseball Rules 5.05(a)(5)-(9), 5.06(b)(3)(C) Comment, and 5.06(b)(4)(F) (formerly Rules 6.09(d)-(h), 7.04(c) Comment, and 7.05(f)), respectively), the Replay Official shall place the base runners on the bases he believes they would have reached had the reviewed call been made correctly. (For example, Official Baseball Rule 6.01(e) Comment (formerly Rule 3.16 Comment) states: "Batter and runners shall be placed where in the umpire's judgment they would have been had the interference not occurred." Rule 6.01(h)(1) (formerly Rule 7.06(a)) states: "[A]ll runners shall advance, without liability to be put out, to the bases they would have reached, in the umpire's judgment, if there had been no obstruction.") Any doubt regarding the placement of runners should be resolved in favor of the last base legally touched at the time of the challenged call. More than one base should not be awarded unless it is obvious to the Replay Official that a runner would have safely advanced beyond one base had the call been made correctly, or the Official Baseball Rules otherwise require such advancement.
3. Factors to Consider. The Replay Official should consider several factors when placing the runners, including: (a) the depth of fly balls; (b) the speed of runners; (c) the location of runners on the field when the play occurred; (d) the number of outs at the time of the play; and (e) whether the incorrect call affected the subsequent behavior or conduct of the offensive or defensive players.

If the reviewed call had been made correctly, this would have been a double play. Is it a double play after review?

Thank you !