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It appears that the majority of the issues stem from people using either fake, altered or erroneous identities when registering.
This is in breach of their terms and conditions which specifically state (these are their old terms and conditions from when people signed up).
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Use of the Platform As a condition of your use of the Platform, you represent and warrant to, and covenant with TradeSatoshi that: (a) you have reached the age of majority in your jurisdiction of residence; (b) you possess the legal authority to create a binding legal obligation; (c) you shall use the Platform in accordance with these Terms of Use and all applicable laws; and (d) all information supplied by you on the Platform is true, accurate, current and complete.
While is sympathize with people in this predicament it is a common thing people tend to do when they try to use a website using a false identity. (Give partially inaccurate or completely inaccurate identity).
I would recommend spending some $ and finding out the registered address of the exchange and sending a letter explaining the situation and providing written proof of identity.
It is possible that they checked the identity on a database and found no match. A lot of exchanges are forced by law to start KYC. Even some of the decentralized exchanges are on the radar of law enforcement.
I haven't personally used Tradesatoshi for more than a year so I can't comment on whether much has changed.
The issue you're talking about is: User agreed to pass the KYC-check, but the personal information, provided by him earlier was innacurate, so he can't complete it. This is only one aspect of this story.
But this is not the case, i'm talking about.
From one side, the exchange can ask for a mandatory KYC-check (normally with a notification in advance, which was not done by Traidsatoshi).
From the other side, user can deny to pass it. In that case he won't be able to trade anymore - this is ok. But, all the funds he had before KYC were deposited or traded by him under the Level 1 verification from Tradesatoshi, so they are all legal. So all this funds must be returned to the owner. By now the affected Tradesatoshi users are denied the right to withdraw their funds, which is totally unacceptable!