Disproof
The story advances a recurring pro-Kremlin narrative painting Ukraine as a crumbling state, too weak and divided to make its own strategic choices and thus forced to serve as a US client state.
As a large and politically diverse country, independent Ukraine has elected six presidents since 1991, each with his own set of domestic and geopolitical priorities. Thus, the tenure of both Leonid Kravchuk (1991-1994) and his successor Leonid Kuchma (1994-2005) were periods of "multi-vector" balancing between Russia and the West; the pro-Western Viktor Yushchenko (2005-2010) was succeeded by pro-Russian Viktor Yanukovych (2010-2014) who, upon his flight in disgrace from Ukrainian politics (and from Ukraine), was replaced by Petro Poroshenko. The latter was elected on a firm pro-EU platform and anti-Kremlin rhetoric during a period of large-scale military aggression by Russia.
The current Ukrainian president is Volodymyr Zelensky (elected in 2019), whose foreign-policy platform emphasises de-escalation of the ongoing Donbas conflict, rapprochement with and eventual membership in NATO, and joining the EU.
See here for more cases painting Ukraine as a country under external control.