Op-Amp appears to be stable when operating below the minimum gain specified on the datasheet?

I've been testing this circuit configuration with the THS4021 op-amp, which is "stable at a gain of 10 (-9) or greater" according to its datasheet, and I can see that it's true for certain low gains. There is a lot of voltage oscillation at the output when R1 is set to a value below 200 ohms, but for R1 = 250 ohms or 300 ohms for example, the circuit seems to work fine and I get no oscillation in my output. Why is that? And does that mean I can use this exact set-up in my design or should I select a different op-amp if I am looking for a gain of -4 V/V? I've attached the waveform for reference.

It may work with a specific op amp, but the next device (even of the same type) might oscillate.
You never design outside the design specs of a device (unless you don't care if the design works reliably under all conditions).
Use an op amp that's stable down to a gain of 1.

Try adding a low value resistor in series with pin 6, to reduce the slew rate of the final output signal.
eg. Something like 10R or 100R.

You could also add a low value cap, 10pF - 100pF or more between output and -input, either directly or in series with another low value resistor.

1--"stable at a gain of 10 (-9) or greater"
2--Why R121, R31. That is not good.
3--C1? This amp is not happy driving a capacitor. " Therefore, for capacitive loads of greater than 10 pF, it is recommended that a resistor be placed in series with the output of the amplifier, as shown in Figure 33. A minimum value of 20 Ω should work well for most applications. For example, in 75-Ω transmission systems, setting the series resistor value to 75 Ω both isolates any capacitance loading and provides the proper line impedance matching at the source end."
Do you really need this fast of a amplifier?