Точно!!
Думаю, вопрос закрыт, а мне надо подумать о версиях 1.5.*, хотя рановато, конечно, для продакшна. :(

syntax: ssi_last_modified on | off;
default:
ssi_last_modified off;
context: http, server, location
This directive appeared in version 1.5.1.
Allows preserving the “Last-Modified” header field from the original response during SSI processing to facilitate response caching.

By default, the header field is removed as contents of the response are modified during processing and may contain dynamically generated elements or parts that are changed independently of the original response.