Nothing in the statement from Digital Ocean indicates that they won't kill your account or shutdown your systems - that's not the sort of cloud host any company can afford to use.
Cloud providers that kill accounts - or SAY they kill accounts, must be dropped and not used.
The worst thing that should be possible is for your account to be suspended.
AWS, if there is a billing issue, prevents you making changes to your infrastructure via the console until the billing issue is sorted out - this is good and reasonable.
""Peer review of account terminations. For any account appealing a lock, two agents will be required to review the submission prior to issuing a final deny.""
- I can imagine how this plays out:
(service agent 1 turns to next service agent along) 'This looks like a bad account - I think I should shut it down, what do you think buddy?'
(service agent 2) - 'Yep I trust you, shut it down.'