The replay officials' interpretation of this play was correct. And while you have no reason to trust me, I actually did look up this rule earlier in the season so I already knew about it.
The rule is the ball gets spotted either where it went out of bounds only if the player is airborne. Otherwise it is spotted with forward progress regardless of where it crossed the sideline.
Normally, when a player is going out of bounds in a situation like this, they dive with their whole body off the ground and the ball is spotted where it went out. However, in this case, Bowers had a hand down in the field of play so the ball is spotted at its forwardmost point, even though the ball had already crossed the sideline.
Here is the relevant rule from the rulebook:
Note that it specifies the ball is spotted where it crosses the sideline only if the runner is airborne. That is stated as an exception in contrast to how it is spotted if the player is not airborne.
Now here is Bowers on that play. Note that his hand is down in the field of play, so he is not airbone and thus the ball is not spotted where it was when it crosses the sideline.