I think I have a better way to fix this issue. The events file game_start.txt only looks for the country flags for human civilization. My guess is that those human flags are lost when editing the civilization. So I've replaced this check with one that checks for the Sol system itself instead, which is also flagged by default.
So I've replaced:
limit = { NOT = { any_country = {
has_country_flag = human_1
has_country_flag = human_2
} } }
with:
limit = { NOT = { any_system = {
has_star_flag = sol_system
} } }
and it seems to work at first sight.
I've uploaded the edited file as a mod here:
http://www.mediafire.com/download/ewxglt4wmimm7wb/only_one_sol_system.zip