While this "permission" is interesting, it doesn't mean Putin approved it:
A Russian tycoon believed to control Russian mercenaries who attacked US troops and Kurd allies in Deir Ezzor told Syrian officials he would give Bashar al-Assad a "good surprise" days ahead of the assault, the Washington Post has reported.
Yevgeniy Prigozhin was also in close contact with Russian officials before the attack and told a Syrian official that he had "secure permission" from a Russian minister for a "fast and strong" action that would happen in early February, according to intercepted communications seen by the Post.
On 7 February, pro-Assad troops, including Russian military contractors, advanced on a gas field in the northern Syrian village of Tabiya under the control of the US-backed Syrian Democratic Forces, and were attacked by US-led coalition forces.
The fact that Russia has downplayed the incident shows that the highest levels of Russian leadership didn't approve of the mission--or are so cynical that they approved it to see if they could get away with it while fully willing to abandon the people involved if America resisted.
I prefer the explanation that counts on Russia being a developing autocracy, but with centers of power that aren't always in full compliance with Putin's orders or wishes of the moment.
Really, somebody lower level might have thought they could gain Putin's favor by presenting him with a glorious victory, and when they managed this debacle were disavowed to avoid giving America a glorious victory over Putin.