It absolutely does. Air density affects the structural ability of the system to reach that frequency (based on the stiffness modulus of the component, plus the mass balancing of the attached control surface) in the first place. That's why
Vne is a true airspeed.
Aeroelastic behavior is affected by the medium because it [the medium] acts as a damper, with the flight structural component in question acting as a spring. As the dampening coefficient changes (reduced) with density loss of the medium, the aircraft attains the first flutter point at a lower dynamic pressure (aka higher TAS at altitude) than if it were flying in higher density and higher parasitic drag for the same powerplant (lower altitude). For small conventional subsonic spam cans this flutter point is often not possible at low altitude due to said parasitic drag and high dampening coefficient, even at high dynamic pressure (high IAS). Which is a technical way of saying you'll reach other failure modes first (likely 1st order divergence).
But at high altitude and lower damping coefficient, it becomes easily attainable to reach flutter on the same structure and powerplant, with much lower dynamic pressure required. That's why you generally can't up-power (or even significantly turbonormalize) kites like the RV case study you mentioned in your post. Not because they can't handle it down low, but because they can't up high due to air density effects on structural dynamics aka aeroelastics.
Also recognize the calculation of Vne in many small aircraft does not correspond to flutter as the failure mode, which is why they get away with spoon feeding you with a Vne posted as an IAS/CAS. This kind of "paternalistic lying" is done often for the benefit of knuckle dragging pilots, just like they simplify G-load limit ratings as a fixed range (+3.8, +4.4 et al) regardless of weight, when if one ever cracked open a structures book it would be immediately apparent the structure's G-rating changes with carried weight. Hell, Piper at one point straight up published non-altitude compensated power tables for their turbo installations (turbo arrow with fixed WG). On a Conti no less, which is borderline attempted murder in my eyes
Depending on the airframe, Vne could be reflective of simple 1st order structural divergence (aka the Acme cartoon wings flying off the Wyle Coyote rocket), or sometimes mere control reversal speed, which could occur before flutter failure itself. Other times, flutter could indeed be the first mode of failure, but that speed would be published as a
true airspeed.
In fairness I did not stay at a holiday inn, but aeroelastics was my sub-concentration at Purdue for my M.S.A.E. That degree and a buck twenty gets me a cup of coffee, and I'm still the idiot in the room for having done that instead of going to Arizona State for basket weaving, where the girls are twice as hot, half as smart and thus twice as likely to ------- me.