Really out of memory?

I have a linux postgres server in the field. Its version is:

PostgreSQL 8.2.4 on i686-redhat-linux-gnu, compiled by GCC gcc (GCC) 4.1.1 20070105 (Red Hat 4.1.1-51)

(aka postgresql-8.2.4-1PGDG)

A few days ago, its log started showing this:

May 31 02:59:40 sfmelwss postgres[30103]: [1-1] ERROR:  out of memory
May 31 02:59:40 sfmelwss postgres[30103]: [1-2] DETAIL:  Failed on request of size 16777212.
May 31 03:02:40 sfmelwss postgres[31490]: [1-1] ERROR:  out of memory
May 31 03:02:40 sfmelwss postgres[31490]: [1-2] DETAIL:  Failed on request of size 16777212.
May 31 03:05:40 sfmelwss postgres[31913]: [1-1] ERROR:  out of memory
May 31 03:05:40 sfmelwss postgres[31913]: [1-2] DETAIL:  Failed on request of size 16777212.

That seems pretty self-explainitory. But I'm not so sure, because SAR
says:

02:30:01 AM kbmemfree kbmemused  %memused kbbuffers  kbcached kbswpfree kbswpused  %swpused  kbswpcad
02:40:01 AM     13332   1003316     98.69    130448    198188   1034572     13996      1.33        32
02:50:01 AM     17116    999532     98.32    128708    196384   1034596     13972      1.33        44
03:00:01 AM     16372   1000276     98.39    129128    196388   1034596     13972      1.33        44
03:10:01 AM     17220    999428     98.31    128268    196828   1034736     13832      1.32       132
03:20:01 AM     14416   1002232     98.58    130464    197348   1035224     13344      1.27       152
03:30:01 AM     16292   1000356     98.40    127604    196684   1035700     12868      1.23       168

...which indicates there was still plenty of space left in swap. Now, I
realize I don't want to be actually using my swap, but I'm wondering if
the out of memory messages are a red herring. Should I be looking at
something else, like the number of processes, open files, or shared memory
segments?

FWIW, I have disabled the OOM killer (but not, as I understand it, my
swap space) by setting:
vm.overcommit_memory = 2
vm.overcommit_ratio = 100