  Small collision systems, e.g. $p$-$p$ and $p$-Pb collisions, comprise a
potential reference for more-central A-A collisions with regard to production
(or not) of a thermalized quark-gluon plasma (QGP). Small systems with low
particle densities should evolve according to simple QCD mechanisms including
projectile-nucleon dissociation and dijet production. But it is now claimed
that QGP may appear even in $p$-$p$ collisions based on apparent evidence for
radial flow from shape evolution of $p_t$ spectra and from variation of total
yields for strange and multistrange hadrons relative to statistical models. The
present study confronts such arguments with a detailed analysis of $p_t$
spectra for strange and multistrange hadrons from 5 TeV $p$-Pb collisions and
13 TeV $p$-$p$ collisions via a two-component model (TCM) of hadron production.
Based on previous analysis of lighter hadrons the TCM accurately predicts
spectra for Cascade and Omega hadrons. Significant results include multistrange
hadron spectra dominated by jet fragments, variation of strange-hadron
abundances exaggerated by certain plot formats and spectrum extrapolations, and
detailed relations between ensemble-mean $\bar p_t$ evolution with event charge
density and small shifts of jet fragment distributions on $p_t$. Within the
context of the TCM, $p$-$p$ and $p$-Pb collision systems with comparable jet
contributions are found to be equivalent within data uncertainties. Attribution
of certain data features to radial flow is falsified.
