Publicize itself actually doesn't add any elements to your site's frontend, so you can keep using Publicize without any issues.
The Sharing module, however, will indeed add some elements to your site as soon as you add sharing buttons to the bottom of your posts. Whether it's with Jetpack or any other plugin, as soon as you add third-party services to your posts or to your sidebar each one of these services will have to make outgoing calls and that will have an impact on your site.
The 2 links you referred to are used to update the counters next to the sharing buttons appearing at the bottom of your posts:
http://i.wpne.ws/TDUd
To solve the issue, you can just remove the buttons or deactivate the sharing module altogether by following the instructions here.
Another solution, and if the buttons are important to you, would be to accept the performance impact and focus on another element of the Pagespeed insights. Here are some examples of things you could work on:
- Use a CDN to offload some of your content to external services that have better loading times than your own server: http://codex.wordpress.org/WordPress_Optimization/Offloading#Commercial_Services
- Remove extra plugins that add resources to your site. As an example, you're using a Contact Form plugin, when Jetpack already includes its own Contact Form module. You also use a plugin to display the admin bar to all your visitors. This admin bar includes different javascript and CSS files that have an impact on your site's performance.
- Use a caching plugin like W3 Total Cache or WP Super Cache.
- Use web-safe fonts in your theme instead of using Google Fonts, thus saving extra calls to the Google Font servers
- etc
I hope this helps.