  We investigate the explicit role of negative local non-Gaussianity, $f_{\rm
NL}$, in suppressing the abundance of primordial black holes (PBHs) in the
single-field model of Galileon inflation. PBH formation requires significantly
enhancing the scalar power spectrum, which greatly affects their abundance. The
associated frequencies in the nHz regime are also sensitive to the generation
of scalar-induced gravitational waves (SIGWs) which may explain the current
data from the pulsar timing arrays (PTAs). Our analysis using the threshold
statistics on the compaction function demonstrates that Galileon theory not
only avoids PBH overproduction using the curvature perturbation enhancements
that give $f_{\rm NL} \sim {\cal O}(-6)$, but also generates SIGWs that conform
well with the PTA data.
