I agree that it seems counterintuitive. That was my understanding based on this article, which doesn't distinguish UFA's in terms of whether or not they were on a protected list. Perhaps the article wasn't precise enough or maybe I read it incorrectly.
Expansion Draft Primer: What's Exclusive Free Agency?
The team is expected to have an exclusive negotiating window with free agents during the expansion draft - that could potentially be 48 hrs.
This would mean that before other teams can begin scooping up existing NHL players, Vegas would have the opportunity to get a head start.
During this two-day stretch, the only team that would be allowed to sign active NHL players is the Golden Knights.
The only catch is that if Vegas signed a player who most recently played for Team X, the Golden Knights would no longer be able to select a player from Team X in the Expansion Draft.