Maybe the online help for tabstat contains an error?
--snip--
Description
...
With the by() option, tabstat resembles "tabulate varname,
summarize(varlist)" in that both report statistics of varlist for
the
different values of varname. tabstat allows more flexibility in
terms of
the statistics presented and the format of the table.
--snip--
tabulate varname, summarize(varlist) or tabsum does not take a varlist
for the summarize option.