  Pulsar timing arrays (PTAs) are presently the only means to search for the
gravitational wave stochastic background from supermassive black hole binary
populations, considered to be within the grasp of current or near future
observations. However, the stringent upperlimit set by the Parkes PTA (Shannon
et al. 2013, 2015) has been interpreted as excluding at $> 90\%$ confidence the
current paradigm of binary assembly through galaxy mergers and hardening via
stellar interactions, suggesting evolution is accelerated (by stars and/or gas)
or stalled. Using Bayesian hierarchical modelling, we consider implications of
this upperlimit for a comprehensive range of astrophysical scenarios, without
invoking stalling nor more exotic physical processes. We find they are fully
consistent with the upperlimit, but (weak) bounds on population parameters can
be inferred. Bayes factors between models vary between $\approx 1.03$ -- $5.81$
and Kullback-Leibler divergences between characteristic amplitude prior and
posterior lie between $0.37$ -- $0.85$. Considering prior astrophysical
information on galaxy merger rates, recent upwards revisions of the black
hole-galaxy bulge mass relation (Kormendy & Ho 2013) are disfavoured at
$1.6\sigma$ against lighter models (e.g. Shankar et al. 2016). We also show, if
no detection is achieved once sensitivity improves by an order of magnitude,
the most optimistic scenario is disfavoured at $3.9\sigma$.
