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See title. I was under the impression that they couldn't (due to deepstrike rules) but I saw a battle report or two where they did. Was this played wrong in the videos? Was there an faq or something that allows them to move or charge the turn they are summoned?

The Blood Tithe Table rules tell us, "When a rule indicates that a unit is summoned, a new unit under your control immediately arrives via Deep Strike within range of the specified unit(s) on the board."

As you say, Deep Strike tells us units arriving as such cannot move in the Movement phase or charge in the Assault phase, although they can Run in the Shooting phase.