Why do we use different arguments for determining the strength of hydracids and solubility of ionic compounds?
When pondering solubility, you can't just think about what happens to the compound, you have to think about what happens to the solvent, too.  Solubility is a balance between the loss of interactions between the particles of the compound and the gain of interactions between those particles and the solvent particles.

In this case, the small highly charged F- anion will have much stronger ion-dipole interactions with water, as reflected in its much higher heat of hydration (-524 kJ/mol for F- versus -308 kJ/mol for I-).  That suggests to me that even if the lost Ag+/F- interaction (whether defined as "ionic" or "covalent") is greater than the equivalent lost Ag+/I- interaction when AgI dissolves, the much strong interaction of the F- with water more than compensates, giving AgF the greater solubility.