Quick- Hostgator are killing my sites!

Definitely sounds like a permissions problem.

But different files need different permissions.
So it depends what the WP logic does with each file, doesn't mean that
if one WP install has some permission, that all use the same. Though they might.
When accessing some files, the web server usually does is as user "nobody"
... on my box it's user "www-data" which is just a low-privilege user
for security reasons. Low privileges are needed to limit the damage
someone can do ... in case server gets hacked by unauthorized martian.

Permission 755 means:
owner group other
[rwx] [r-x] [r-x]
and your server comes here as an "other" user at runtime.
'rwx' stand for read/write/execute permissions, hence
755 gives your server read and execute permission over some file.
Your error means that the server failed to do some stuff because
it lacks one of those permission: add read AND execute
permissions to the "other" user, and that should solve your problem.
Hope my explanation did not gave you a headache, it's actually
much less harmful that it appears... good luck!!

PS. Careful with the "write" permissions: do not give it to any "other" user
as that means that anyone (with a bit of knowledge) is then authorized
to modify and delete the file with that permission. You sometimes need to give
those permissions so low-permission users (like your web server)
can write stuff on the HD, but be careful with those.

Conclusion: setting permission 755 to your file "index.html" should solve
your problem. If it does not, check the permissions of the directory/folder
containing the index.html file, as the permissions of that may have "read"
permission disabled... anyway: try to find who is preventing your server
from reading the index.html file, then correct that with appropriate permissions