In a PLL frequency synthesizer, the RC network controls loop response, not frequency accuracy. The PLL synthesizes a new frequency based upon the input reference frequency, so the output frequency has the same accuracy as the reference frequency. However, the input and output will usually have different amounts of jitter.
By the way, low-cost programmable clock oscillator chips usually contain a crystal oscillator (fixed reference frequency) plus a PLL synthesizer that generates the desired output frequency.