That is to be expected since there's circuitry in parallel with the cap.
But I thought the whole point of LCR/ESR meters was their ability to test components while they are still in the circuit?
Afraid not. That would be quite a device if it could figure out the topology of the circuit, identify the components that are interacting with the one being measured, interpret the behavior of said topology and components, and then infer what the correct value
should be rather than the value that is measured.
As a simple example, if you're given a black box with two terminals to measure the capacitance inside, how can you tell how many capacitors there are without looking in the box? You can measure the total capacitance value, but that could be the result of one or a dozen capacitors. Suppose that you open the box and find that there are five capacitors in parallel. How do you measure the value of the middle capacitor? What about the left-most one?
The only reliable way to measure an individual component is to do it in isolation. In-circuit measurement can be useful if you understand the circuit, what you're measuring, and what you're not measuring, in order to get an idea what may be faulty. Then, you confirm your hypothesis by re-measuring out of circuit.