Typical X7R caps are 1 GΩ-uF or 1 uF = 1 GΩ , 10 uF = 0.1 GΩ or 100 GΩ max
The MCP1703 specs are given in the table for specific conditions and measured by the ground current.
With 12V in and 5V out your load leakage = 80uA
Your DMM sees a 150 kOhm Req load when the spec is 12V/2uA= 6MΩ
Next apply a resistive load of 50mA on output to see if there is any spurious issue with no load. e.g. 5V out/50mA = 100 Ohms Expect Regulator ground current to be 30uA. If your current drops from 80uA to 30uA, then you may have a spurious oscillation in your layout of linear regulator.
So the IC does not appear to meet spec.
simulate this circuit – Schematic created using CircuitLab
Make sure your assumptions the test set does not induce this leakage with jumper wires from In to out in place of IC.
If that proves valid, then.... Consider (1) ESD damage and discount if careful, then...
Write to Distributor about defective parts and get an RMA. Return Material Authorization or choose better parts.