Regardless of what does or doesn't happen in the pedal pictured, what gets called treble and bass in pedals can vary substantially in terms of what it does and how it does it, much the same way that what gets called "stereo" can happen in a multitude of ways. That's not to say that anyone is cheating in their naming of controls. Rather, you spot a way to change tone, and you ask yourself "What would I call it so the control made sense to the minimally informed user?", and the answer comes back treble and bass. Some pedals have Baxandall-type boost/cut controls, where others have simple cut like a Fender/Marshall tonestack.
One fairly simple way to get adjustment of the bottom and top end in an overdrive pedal is to use dual paths. For instance, in many of Joe Gagan's designs, you'll often see two parallel input caps, one with a variable resistor in front of it. The "pot-assisted" cap is always much bigger than the other one. As input caps, these limit the low end of the device up front. As the pot resistance in front of the larger cap is reduced, the smaller-value cap plays less and less of a role in determining that low end limit, and the low end is set by the combined parallel capacitance of the two caps. So, in a sense, that pot ahead of the larger cap acts like a bass trim/cut control. Other than the pot itself, only a single extra part is used. If the pedal has other sorts of tone shaping downstream that trim the treble to achieve some sort of tonal balance, such a control may feel like a bass boost control, rather than bass restoration.
Another type of dual-paths approach is one you'll often see in pedals that employ pre-emphasis/de-emphasis for noise reduction, or simply to alter the tonal balance in some manner. If you look at the standard non-inverting op-amp, the gain is set by the joint action of the feedback resistance and the ground resistance (from inverting pin to ground). The op-amp doesn't particularly care if each of those two resistances comes from a single resistor or a hundred. However, the bandwidth of the op-amp is affected by the joint action of each of those resistances and their associated caps; being the feedback cap in one case and the cap to ground in the other. If two paths to ground are provided, each through a different value cap, it is possible to provide two separate bandwidth products, one of which can be varied to achieve treble boost..
So, say I have a 470k feedback resistance, and a 10k resistance to ground, through a 0.1uf (100nf) cap. This will give a gain of 48 and a low end rolloff starting around 160hz. Suppose I provide a second path to ground, though, using a 2k2 resistor and a .047uf (47nf) cap. The low-end rolloff of these two parts will begin around roughly 1540hz. But here's the kicker: the gain for content above that point will be roughly 214!! That's some kinda treble boost. The high end will, of course take the path of least resistance...literally, such that you'll have a relatively flat response from 160hz up to just over 1500hz, and a serious boost above that.
You can probably see where I'm going with this. Make that second resistance variable, and you can futz with the degree and range of high-end boost. Once again, apart from the pot itself, we've only added a cap and resistor (you'll need a minimum fixed resistor value to prevent instability).
Now, I'm not saying that this is what is in the timmy (if it's Paul's bread and butter, I certainly hope not), but it IS a way to achieve what could be *labelled* as treble and bass functions within the context of an overdrive pedal, without a lot of fuss, space, or fancy design, which was Vanessa's original request. Is it "treble" or "bass" of the same type found on a car stereo or an amp? Not at all. Does it have that same degree of flexibility? Hah, you wish! Will it change how your top and bottom end behave in the context of overdrive? Absolutely.
