I am going with no on that, there are too many Machiavellian concepts in there to buy.
1. How does this make Putin look stronger?
An army of several thousand armed rapists an murderers drove from Ukraine to Rostov, took over a city, shot down half a dozen Russian aircraft then drove to a few hours outside Moscow before sobering up and not one Russian unit even attempted to stop them.
2. Putin packed his bags and headed to St Petersburg rather than hang around.
3. That dimwitted muppet from Belarus did all the negotiating.
Surely even the most ardent Putin fan would have to ask why the army made almost no attempt to stop them, had Putin wanted to look like the strong leader he would have stayed in Moscow and organised forces to stomp on an insurrection not run and hide waiting for a third party to intervene.
Another sign of weakness is that he made a couple of speeches stating that the leaders of this "betrayal" would be held accountable and yet Prigozhen is in and out of major Russian cities still.
My guess is that the FSB story is correct, Prigozhen planned this but word got out early to the FSB so in a drunken fit he went ahead early, Putin discovered no one in the Russian military was going to save him (not even his CSTO allies) and got Lukashenko to broker a deal.
1 The Wagner group is more than an army of armed rapists and murderers
2 That no Russian unit attempted to stop them can have as reasons that
A The advance of the Wagner group was not considered as dangerous :Moscow has more than 12 million inhabitants and can thus not be captured by a few thousand men .We don't know how many men of the Wagner group were going from Rostov to Moscow ,a distance of 1083 km and we don't know how close they were to Moscow .
B the Kremlin tried, for political reasons ,to prevent a fight with a lot of casualties that would be used by the Western propaganda as a proof that there was a civil war in Russia .
3 There is no proof that Putin backed his bags and left Moscow .
4 Lukachenko is not a dimwitted muppet
5 There is no proof that this operetta rebellion was a serious danger for the Putin regime .
6 The bosses of Wagner are in Belarus ,but no one knows where the other members of the Wagner group are . Rostov?Belarus ?Ukraine ? POW camp ?
7 There is also the point that no one knows the reason for this operetta rebellion. Some claim that there was a strong hostility between Prigozhen and the army top .
8 And no one knows why suddenly ,after one day, the rebellion collapsed .
9 It is also an exaggeration to say that the Wagner group captured Rostov (population : 1,1 million )
10 I would not say that Prigozhen planned the whole thing,reality is that it was an improvisation .