There certainly were different political shenanigans, but your other theory isn't wrong either. I'll repost my answer from very similar topic and also add that this difficult political situation also led to some Russian armies conducting themselves very passively - they knew that Russian empress was ill and waited for her successor to take the throne and tell them what to do next.
Peter III withdrew because he (and - coincidentally - his wife, future empress Catherine) was pretty much against Prussophibic position of his aunt and then-empress Elizabeth. Peter, being German born and raised, was also big admirer of Frederick the Great, whom his aunt greatly despised (the feeling was mutual). Reasons for outright hatred of Russian empress towards Frederick vary, but the only theory I'm accustomed with in details says that Frederick and Elizabeth mistrusted each other as Elizabeth feared his concernments towards her essentially rebellious accession while Frederick, knowing that Austria had been considered to once again become possible Russian ally (since their wars with Turkey in the first half of 18th century), rightfully feared Russian military engagement in his wars in Europe.
Peter, who never learned to properly speak Russian and didn't really felt he was suited for his future position of the emperor, was opposing his aunt at every turn. He possessed great love to all things military (which wasn't complemented by his martial abilities though), and overmilitarized and, most notably, distinctly German, "civilized" Prussia was his personal picture of the perfect state. Fredreick in turn was like a big brother he never had, and just an idea of Russia (a country he never loved, a country that was essentially foreign to him) going to war with such an idol was outrageous in his opinion. Even being a grown up man, he would sometimes lock up in his own room and reenact military engagements with toy soldiers, imagining himself to be Frederick's greatest assistance. For these exact reasons he enlisted a small company of Holstein mercenary soldiers in early 1750s (which later was reformed into a thousand man strong regiment in 1758) which were to become his own personal guard and something akin to substitute for his old toy soldiers. He imagined himself to be next great conqueror and planned to crown himself - just like Frederick did - after a successful military campaign aimed at Denmark: his father, count of Holstein, was very bitter after Denmark occupied and took Shleswig away from him in the Great Northern War, and had great hopes that his son would one day triumphally return these lands to their county (this also played big role in Peter's obsession with army).
After Elizabeth died, first thing done by Peter once he ascended the throne was to conduct peace talks with Frederick. His actions effectively nullified all Russian gains in the Seven Years War and since he never was very popular due to aforementioned reasons to begin with, this provoked nobility to plan a coup to overthrow him. His poory thought out idea of a joint war against Denmark (that never had any serious tensions with Russia) together with Frederick was even more insulting. Especially considering he was dreaming of personally leading the guard in charge, and Russian Guardsmen, being somewhat reminiscent of Roman Praetorians, weren't fond of the idea to risk their lives since they've been absent from wars for a long time by this point. Radical misunderstanding of the court politics would be his undoing. In coup d'etat in 1762 he was deposed and later died in captivity.
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