The source of the noise at any given moment is where the tire is (or has just caused) the strip to vibrate. That point is moving away from the observer about as fast as the car is moving away from the observer
So, the doppler effect is present since the point of friction is moving to a different point on the road, even if the road is stationary.
I'll add one thing: normally you hear Doppler effect with a nearly constant sound (emergency sirens.) Here the pitches are changing, but because our minds instantly recognize the 8-step Western scale we can pick out the frequency shift even though the frequency changes between the different notes may be the larger change.
I think your explanation is correct, apart from that i do not think it is the tire that causes the strip to vibrate as much as it is the strip that causes the tire to vibrate.
If it is the tire that makes the noise, it is no surprise that there is a Doppler shift.
I don't think the tire is vibrating at an audible frequency. The tire colliding with the road creates a burst of air, and since these 'bursts' are moving you have a doppler effect.
In theory you could create the same effect by setting off fireworks.
> It's interesting how you still observe the doppler effect even though the road isn't moving
Relativity. Christian Doppler's equation for the change in frequency of a wave, for subsonic velocities, is approximated by three variables: the velocity of the receiver relative to the source, the velocity of waves in the medium and the emitted frequency [1]. The first term is symmetric between a source approaching the receiver and a receiver approaching a source.
(The actual equation measures the velocity of the source and the receiver relative to the medium. Here, too, the symmetry between a source moving towards a receiver, the latter un-moving relative to the medium, and a receiver moving towards a source, the latter un-moving relative to the medium, is preserved.)
The source of the noise at any given moment is where the tire is (or has just caused) the strip to vibrate. That point is moving away from the observer about as fast as the car is moving away from the observer
So, the doppler effect is present since the point of friction is moving to a different point on the road, even if the road is stationary.