[Nathanael Rosenheim]

Thank you, Jessica, Clyde and Kreshna. I ran into this same problem and found the statement in the help file curious.
I modified the provided code and demonstrate that it does work:

lear all
set more off
macro drop _all
scalar drop _all
set seed 123456

capture program drop test
program define test, rclass
syntax [, nobs(integer 10)]
   preserve
   set obs `nobs'

   scalar state1 = substr(c(rngstate), 1,    2000)
   scalar state2 = substr(c(rngstate), 2001, 4000)
   scalar state3 = substr(c(rngstate), 4001, .)

   g x = rnormal()
   sum x, mean
   return scalar x_avg = r(mean)
   restore

   capture post buffer (r(mean)) (state1) (state2) (state3)
end

postfile buffer double x_avg str2000(state1 state2 state3) using results, replace
simulate, reps(3): test, nobs(10)
postclose buffer

use results, clear
gen strL state = state1+state2+state3
drop state1 state2 state3


* Demonstration that the each replication can be replicated
local selectstate = state[2]
set rngstate `selectstate'

test, nobs(10)
return list