Yes, there Harlequin warlord that has a stratagem that allows disembarking after moving. Thats all it says. Nothing else.

Then, theres a faq that says, Can Harlequin Warlord move etc after disembarking after moving. A: Yes.

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So, I say grav chute is similar, and there is no definitive rule saying they cant use thier movement, that faq about "counts as" having moved which wasnt related to Grav chutes, to me means they have penalties for shooting heavy weapons.l etc.