I think it very much depends on the meter. Some meters are true L/C/R meters only, are very crude and only measure charge/discharge time or oscillation frequency in a simple circuit, others pass an AC voltage across the device under test and measure the phase and magnitude of the current. That makes it simple to derive the purely capacitive and resistive components.
As you say though, that is just at one frequency, and both R and C values can change massively with frequency. A cap that looks fine at 100kHz may degrade horribly at 1MHz. Ideally you want to be able to sweep the values, but then you start getting into the realm of scalar and vector network analysers.