Hall (2005) mentions Barro's paper twice, but the first one in p. 51 is in the introduction and in order to alert the reader on what to expect. The essential dialogue between the two papers is in p. 56, where, Hall, after presenting his model and its workings, writes:
"The earlier work implied inefficient outcomes, especially the loss of
a job under conditions where both worker and employer could have been
better off with a wage adjustment. The wage norm I consider interferes
neither with the formation of efficient matches once the parties are
in touch with one another nor with the preservation of jobs with
positive surplus. Inefficient separations cannot occur. As a result,
the model provides a full answer to the indictment of sticky wage
models in Barro (1977) for invoking unexplained inefficiencies in
economic arrangements."
In p. 64 moreover Hall writes
"Stickiness is plausible, because it occurs only within the range
where the wage does not block efficient bargains from being struck and
maintained."
From this second quote, one could indeed indirectly validate the OP's second quote - that in order to provide a rationale for wage stickiness, we should restrain ourselves to cases and models where wage stickiness, in order to arise does not require blatant inefficiency of the contracting parties (because, after all, "blatant inefficiency" can explain everything).
The important remark here is that not all sticky-wage outcomes are necessarily inefficient.
But this essentially concurs with Barro's (1977) approach: Barro criticizes specific sticky-wage models where contracts have provisions only on the wage and not on the level of employment (or they have arbitrary such). Barro shows that not providing for employment determination may create dead-wight losses for both parties. On the other hand, providing an optimal rule for employment determination (optimal in the sense of "maximizing the pie", as he writes, available to employers and workers), would eliminate this dead-weight losses, and then, the issue of wage determination is to be considered, which may very well imply fixed nominal wages.
pp 311-312:
"Given this form of employment rule, which maximizes the total pie
available to firms and workers, one can then consider optimal (and
competitive) payment arrangements that would determine the split of
the pie. For example, it may be optimal for firms to perform the
insurance function of guaranteeing to the workers, ex ante, a fixed
(nominal or real) wage or income. In this case long-term contracting
may account for ‘rigid‘ wages, and may also explain the apparent
non-wage rationing of jobs."
So, I don't see any change in the interpretation of Barro's paper. Both papers seem to accept that it may be the case that sticky wages arise from optimal, efficient behavior. Barro criticized sticky-wage models available then for not modeling such an efficient way to obtain the stickiness. Hall's accepts Barro's critique on past sticky-wage models, and creates a model where indeed, fixed wages can be a feature of an efficient equilibrium, something that Barro also considers it possible, as the above quote shows.
