Actually that's not the correct explanation, and in fact volumes are(more or less) directly additive when you add together molecules with dramatically different sizes, such as mixing pentane and octane.One molecule larger than the other (regardless of which), would net the same result.
The likely explanation is a lot more nuanced and has to do with the nature of intermolecular interactions in liquid water and how hydrogen bonding causes the molecules to arrange themselves and create "voids" that other molecules can fit in. That's especially true when you involve something like alcohols that will themselves hydrogen bond with water and disrupt the bonding.