There can be a few good reasons to do things less directly:
1. High impedance filters require very large inductors (with very little parasitic capacitance) and very small capacitors; or for transmission line filters, impractically thin traces. A buffer can supply the low source impedance needed.
2. The device's output impedance may not be constant. Typically, a chip's output characteristic will be a follower (low Ri BJT, or modest Ri MOS), or an open-collector (>>10kohms Ri, in parallel with some pF pin capacitance), among other kinds more likely found at lower frequencies (like an op-amp's output, which can be inductive over a wide range). All of these parameters can vary with bias, or with output level.
3. The device may not function properly, if loaded with too much or too little impedance. The datasheet will give a typical application. An example reason would be: too high of a load resistance, on a constant-current type output, develops too much voltage, so that the output device saturates, causing distortion and limiting available output amplitude.
4. The device may not function properly, due to parasitics. Semiconductor capacitances are nonlinear, so a large voltage swing means a large capacitance swing as well.
For these reasons, you'll often find e.g. a DAC or DDS chip, followed by a buffer: if the source is constant-current type, then the amplifier is usually a TIA type amplifier. This gives a low input impedance, minimizing errors (at the expense of adding some noise to the signal path). The amplifier's output is easily matched into the filter's impedance, which can be any modest value (say 50-200 ohms).
If SNR isn't a big deal, the chip's output might be terminated into a resistor, and the filter attached to that. Or instead of just a resistor, a resistor divider (attenuator) might be used, to achieve even more separation between the filter and the IC pins.
Usually, an amplifier follows the filter, necessitating another termination resistor.
If the chip pins are a known, and stable, impedance, the filter can be designed around that, regardless of how high or low the source impedance actually is -- there are filter designs tables for singly-terminated (one side Zo, the other side open (CCS source) or shorted (CVS source)) filters, of all the usual types.
This is the method you were going down before, which works fine if all those assumptions work out (the quality of the output pins, of the inductors and capacitors in the filter, of the filter's load..). Accordingly, if you change any one of them (like, the oscillator!), you'll need to adjust component values to keep things in order.
There's nothing wrong with an oddball system impedance (i.e., other than 50 or 75 ohms), but you need to make sure that at least one end of each network is matched properly. If you're using a significant length of 50 ohm transmission line in a 400 ohm system, you're incurring a lot of capacitance (if the line is short), and at the very least, you'll need to reduce the value of whatever capacitor is nearby to account for it.
If the line is long, you'll have unavoidable peaks and dips, due to the strong reflections from each end being poorly matched. If you can't get/make a line with a low enough impedance, you need matching transformers at each end to convert from line impedance up to system impedance.
Tim