How could chlorine dioxide be stabilized in aqueous solution?
Your assumption is correct. The term “stabilized chlorine dioxide” is misleading since the solution does not contain relevant amounts of chlorine dioxide $\ce{ClO2}$.

The solution actually contains sodium chlorite $\ce{NaClO2}$, which is the salt of the unstable chlorous acid $\ce{HClO2}$. At low pH, chlorite solutions contain chlorous acid 
$$\ce{ClO2- + H+ &lt;=&gt; HClO2}$$
which decomposes to form chlorine dioxide approximately according to
$$\ce{5HClO2 -&gt; 4ClO2 + HCl + 2H2O}$$
or
$$\ce{4HClO2 -&gt; 2ClO2 + HClO3 + HCl + H2O}$$

At higher pH, decomposition of sodium chlorite slows down. Therefore, sodium chlorite is mainly stabilized by using a buffered solution. In your product, the buffer consists of trisodium phosphate and citric acid. Thus, a better description would be “stabilized sodium chlorite” instead of “stabilized chlorine dioxide”.