Which of the following cannot be explained on the basis of Fajan's Rules?

The covalent or ionic nature of a chemical bond can be predicted using Fajans' rule. 
$BaC{O}_{\mathit{3}}$ is much less soluble than ${\mathrm{MgCO}}_3$.
The order of solubility of carbonates is: 
${\mathrm{BeCO}}_3>{\mathrm{MgCO}}_3>{\mathrm{CaCO}}_3>{\mathrm{SrCO}}_3>{\mathrm{BaCO}}_3$
This can only be explained on the basis of lattice energy and hydration energy.
Hence, the option C is correct.