I've read the instructions steps as:
1. Download your entire LinkedIn data.
2. Give us your entire LinkedIn data.
The "larger" data they are asking for includes "... connections, verifications, contacts, account history, and information we infer about you based on your profile and activity ..."
We've added some privacy details here: https://jobsbyreferral.com/privacy.
You absolutely do not need to upload all of your data. Just a CSV in the format we need (which is now updated on the homepage as well).