That's only partially true. The most potent reason for crash is engine failure and USA engines are far ahead of Russian in reliability.
Russian engines are so unreliable that Russia doesn't operate any single engine fighter jet while USA uses most of fleet of single engines f16 and now f35.
The only single engine jet on Russian engines are jf17 and j10 both because of lack of options for chi-pork and both are hanger queens with robust crash records and availability rates down the drain.
Hmm, I wonder if that is the case.
Single-engine vs. double engine doctrine boils down less towards engine reliability, more towards operational doctrine.
Russian doctrine of air to air combat emphasizes mainly upon short-range engagements and dogfights. Reason their air superiority fighters have twin-engines for greater power & T/W ratio, insane maneuverability, and excellent short-range adversary engagement options (R-73 + Sura-K HMS).
Examples - Mig-29/35, Su-27/30/35, Mig-25/31.
Russians did operate single-engine jets, where they think power is not an issue, for example, the Mig-23/27 series.
After the collapse of the Soviet Union, Russia didn't really pay much attention to developing and refining their tech. The reason their engines are still inefficient and smoky but work nonetheless.
Also, at the same time, America and NATO focused upon jets that preserve energy and hence require less acceleration. Their doctrine is towards BVR engagement and minimal WVR & close-range engagement as last resort. Reason in the recent F-35 project, they completely ditched maneuvrability and rather focused upon BVR, situational awareness, and electronic warfare.
To understand the difference between American and Russian jets, take an example of Tesla vs. Ford. While Tesla is obviously superior in performance, it requires daily charging, charging stations, perfect roads for its low ground clearance, timely software updates, and many others.
Ford pickup can be lying in your garage for a year and will still start and run on your first try. It isn't superior to Tesla, but it gets the job done.
Russian engines are so unreliable that Russia doesn't operate any single engine fighter jet while USA uses most of fleet of single engines f16 and now f35.
Fun fact, even though F-16 can hold it's own in air combat, USAF treats them as multirole "bombers", while twin-engined F-15s and F-22s (if available) are used for air superiority.
Regarding the engine, yes, the turbine engine is actually a very critical technology and quite difficult to master. It requires a huge amount of R&D and most of the core technologies are kept secret.
Reason countries like China, Japan, India, and Turkey, although having talent and money required for creating such key-technology, has yet to master the efficiency and sophistication of Turbine engines created by NATO companies, like Pratt & Whitney, Rolce-Royce, Sneccma, and General Electric, who are developing such engines for last 70 years.