Locking the account when the explanation given is inconsistent with the observed behavior it was supposed to explain and the system is again engaing in an apparent DDOS is also a perfectly reasonable action.
It also seems from your posts that both times you were notified of the action by DO, so "not notifying the customer" is not an issue.
I don't see any evidence you were accused of being a "cheap liar", either.
The fact that services now make it cheap and easy to set up servers doesn't mean that you have no responsibility for what the servers you set up do. If you are really running a service with 25K active users, you probably ought to be able to respond to your VPS hosts questions about unusual UDP activity with either an explanation that holds water, or an up-front admission that you don't know where it is coming from and will take action to prevent it, rather than claim it comes from a database dump script that doesn't use UDP.
""" We informed the customer that it may be a good idea to check through the virtual server to see if there were any signs of a compromise just in case """
In fact from the dates listed, it looks like you had over two weeks to check for compromise. Even then, it seems like they tried to talk to you before just closing your account;
""" A second UDP pattern was detected on 2013-09-24 12:27:09 and a ticket was opened 2013-09-24 12:27:14 to request more information from the customer. Because this was already a second occurrence we had to do a more thorough follow up. Discussing the matter with the customer, he informed us that it was a mysql db dump script that was pushing data to dropbox. """
I know this can be difficult, but it's important to understand the difference between calling someone a liar and pointing out that what is being claimed does not match reality.
DO has to take action to protect their reputation, their other customers, and whoever is the target of the potentially malicious attack. If they have empirical evidence of this attack, then they must take action. When you attempted to explain what you thought was the source of the traffic, they took the time to show (in detail) why that was not the case. This is not the same as calling you a liar. It is calling you incorrect, but these are two very different things.
You can be incorrect and not be a liar. That's a valuable lesson to learn if you intend to work in a technical field. If I were you, I'd try to take a step back. Take a couple of days off and come back to the issue. Try to understand why everyone is siding with DO on this, and resist the urge to immediately believe that everyone is against you.
Had you chosen a VPS like amazon, you probably wouldn't even get notified. The first time you'd notice a problem is when you get your $1000 bandwidth bill from amazon.
You're like the customer that shows up at a restaurant and complains publicly about the food and demands a refund. When you make it a public issue, the company will move mountains to help you, but you're still an asshole for doing it.
If DigitalOcean's support wasn't clear about their reasons for suspending the account, or if you feel that you weren't getting a helpful response from them, then post the communications you had with them to prove it.
Your explanation of the events only mentions a single occurrence, at which time your account was locked in addition to the server being shutdown.
In either case, a server engaging in malicious activity, is normally taken offline as soon as the malicious activity is discovered to prevent further damage from occurring. You'd get a similar response from just about any other hosting provider you care to name. If you're lucky, and they're feeling generous, they might work with you to find the problem prior to taking the system offline, but normally standard procedure is to take the system offline immediately. The fact that you seem surprised about this shows you don't have much experience administering your own servers.
The standard response usually goes something like:
1) Server is discovered doing something malicious
2) Server is taken offline/shutdown
3) Administrator is notified
3a) Read only copy of the old server HD is brought online on a new server to allow administrator to perform forensic and backup work*
4) Administrator must bring up new server to replace old compromised one
*Sometimes the provider will provide you the old HD image, sometimes not, really depends on the provider.