Narrow-line Seyfert 1 (NLS1) galaxies are peculiar active galactic nuclei (AGN). Most of them do not show strong radio emission, but recently seven radio-quiet (or -silent) NLS1s have been detected flaring multiple times at 37 GHz by the Metsähovi Radio Telescope, indicating the presence of relativistic jets in these peculiar sources. We observed them with the Karl G. Jansky Very Large Array (JVLA) in A configuration at 1.6, 5.2, and 9.0 GHz. Our results show that these sources are either extremely faint or not detected in the JVLA bands. At those frequencies, the radio emission from their relativistic jet must be absorbed, either via synchrotron selfabsorption as it occurs in gigahertz-peaked sources or, more likely, via free-free absorption by a screen of ionized gas associated with starburst activity or shocks. Our findings cast new shadows on the radio-loudness criterion, which seems to be more and more frequently a misleading parameter. New high-frequency and high-resolution radio observations are essential to test our hypotheses.