Jetpack (Instant) Search: show private posts if user is logged in

#### Steps to reproduce the issue

1. Set up a public site with both private and public posts
2. Do a search looking for a private post
3. Private posts will not show on search results

#### What I expected
The default WordPress search page will show private posts to logged users. I expected Instant Search to do the same and also show private posts.

For context, I have private and public posts mixed on several of my sites and not having access to my private posts by searching for them makes Instante Search _less_ useful than the default search.

#### What happened instead
Private posts are not listed in Instant Search results.

This is compounded by the fact that Instant Search takes over the default search URL making it impossible to look for posts from the public site using any other method unless it is deactivated completely

No files, tests, or entry points are named in the issue. Start by locating the Jetpack Instant Search implementation and its search-result tests, then reproduce the logged-in search against a site containing private and public posts. Done means permitted private posts appear for logged-in users without exposing them to logged-out visitors.

Written by the indexing model from the issue text.