Inductor core saturation: DC vs peak current value!
Saturation isn't a purely DC characteristic; what matters in core saturation is the instantaneous current (technically, the instantaneous H-field).
Whether your application can handle the inductor going briefly into saturation each cycle is another question entirely; I prefer to avoid saturation as much as possible, but that's really not feasible in many applications.
Note that what the inductor can withstand is entirely different from what makes it saturate. Saturation is not a destructive process, and as the current falls they will leave saturation. Saturation and hysteresis do, however, work together to create one of the major types of core losses, so constantly driving it into and out of saturation will cause the core to heat up. This should be accommodated for in your thermal design.
There is also no one current value above which the core is saturated. Specifying a saturation current is the same kind of convenient fiction as specifying a diode's forward voltage; any amount of current will cause a decrease in inductance, but the change in inductance is minuscule at sufficiently low currents, just like the current through a diode is minuscule at sufficiently low forward bias. Most inductors I've seen specify saturation current as the current when the inductor reaches either 90%, 80%, or 50% of its nominal value, referred to as 10%, 20%, and 50% saturation respectively. Make sure you check which one your inductor is specified at!
Here's an example of what I mean:

(source: a datasheet from Magnetics)
This is the saturation characteristics for a magnetic core that's intended to be wound by the designer, not wound at the factory, so it's specified in ampere·turns instead of amperes and \$A_L\$ instead of \$L\$, since they don't know how many turns of wire you're going to put on it. You can see that below about 50 A·t the inductance is roughly constant, but then it starts to fall off as current increases. This is an air-gapped core, which makes the fall-off more gradual than a solid core at the cost of having a lower \$A_L\$, but the same non-instant fall-off is there in any core.