Magnetopause surface eigenmodes were suggested as a potential source of dayside high-latitude broadband pulsations in the Pc5-6 band (frequency about 1–2 mHz). However, the search for a ground signature of these modes has not provided encouraging results. The comparison of multi-instrument data from Svalbard with the latitudinal structure of Pc5-6 pulsations, recorded by magnetometers covering near-cusp latitudes, has shown that often the latitudinal maximum of pulsation power occurs about 2–3° deeper in the magnetosphere than the dayside open-closed field line boundary (OCB). The OCB proxy was determined from SuperDARN radar data as the equatorward boundary of enhanced width of a return radio signal. The OCB-ULF correspondence is further examined by comparing the latitudinal profile of the near-noon pulsation power with the equatorward edge of the auroral red emission from the meridian scanning photometer. In most analyzed events, the “epicenter” of Pc5-6 power is at 1–2° lower latitude than the optical OCB proxy. Therefore, the dayside Pc5-6 pulsations cannot be associated with the ground image of the magnetopause surface modes or with oscillations of the last field line. A lack of ground response to these modes beneath the ionospheric projection of OCB seems puzzling. As a possible explanation, we suggest that a high variability of the outer magnetosphere near the magnetopause region may suppress the excitation efficiency. To quantify this hypothesis, we consider a driven field line resonator terminated by conjugate ionospheres with stochastic fluctuations of its eigenfrequency. A solution of this problem predicts a substantial deterioration of resonant properties of MHD resonator even under a relatively low level of back-ground fluctuations. This effect may explain why there is no ground response to magnetopause surface modes or oscillations of the last field line at the OCB latitude, but it can be seen at somewhat lower latitudes with more regular and stable magnetic and plasma structure.