Part Number: OPA1637
Hello,
I have simulated your circuit. I do not see anything in the simulation that would indicate a violation of input and output signals. However there may be a stability issue.
Tina Simulation File:
I would recommend trying the measurement again but with 102 ohm isolation resistors as shown below. We have these on our EVM for stability purposes. You might be seeing a stability issue.
What are the capacitor types that you are using? Are they COG/NPO or X7R?

Best Regards,
Chris Featherstone