A student investigates a pure hydrocarbon, \(X\), with a measured molar mass of \(56.0\ \text{g mol}^{-1}\). Independent evidence limits the identity of \(X\) to cyclobutane or methylcyclopropane, which are structural isomers. During a combustion analysis in limited \(\text{O}_2\), all hydrogen atoms from the sample are recovered in \(\text{H}_2\text{O}\), but some carbon atoms form \(\text{CO}\). No solid carbon is observed.

Quantity	Measured value
Mass of \(X\) burned	\(0.560\ \text{g}\)
Mass of \(\text{CO}_2\) collected	\(1.320\ \text{g}\)
Mass of \(\text{H}_2\text{O}\) collected	\(0.720\ \text{g}\)

The gas leaving the collection apparatus gives a positive test for \(\text{CO}\). By incorrectly assuming complete combustion and using only the collected \(\text{CO}_2\) and \(\text{H}_2\text{O}\), the student reports an empirical formula of \(\text{C}_3\text{H}_8\) rather than \(\text{CH}_2\). Which statement correctly explains the discrepancy and determines whether a subsequent complete-combustion analysis based only on product masses could distinguish the candidates?