Can I ask what difference it makes to you? Are you a lawyer contemplating bringing a class action suit on behalf of all those whose accounts were unfairly closed?
Different types of closed accounts
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I think he's just curious?
My understanding is that the symbol does indeed indicate "closed because of cheating".
In the cheating forum, the following definition is given:
That cheat icon, tiny blue shirt guy, w/red sign (appears immediately after the avatar), is assigned to the closed account by the site as a 'cheater closed' identifier; It has been noted: #1- Some thus closed accounts later 'lose' the cheat icon (no one has figured why, but is a site controlled thing or software glitch), #2- Certain titled accounts never get the cheat icon, even though indications are that WAS why account closed, again a site decided thing (no glitch).
ALL other closures, by the account holder (own decision), by the site (for myriad reasons, but not cheating) or site determined 'spammer problems' (lots of defines of these) for temporary times, get NO icon identification. (http://www.chess.com/groups/forumview/spotted-account-closures-in-online-chess?page=57)
One respect in which this distinction (account closed with symbol vs. account closed w/o symbol) is important, is the team results of the World League. These team results are corrected for closed accounts. If someone wins a game, but his account is closed later, the team loses this point. But apparently this only holds for accounts closures with a symbol. So it would still be nice to have some official chess.com statement about the criterion for placing the symbol or not.
This has been asked elsewhere already, but I still miss a convincing answer: Apparently there are two types of closed accounts, those with a "account closed" symbol and those without. Here is an example from the World League match Russia vs Holland:
The account KrokodilDandy has been closed and is marked with the respective symbol, the account Cassini-Huygens is closed as well, but without a symbol. What is the difference?
Earlier I thought this meant "closed because of cheating" vs "closed for other reasons", but given the following explanation of the chess.com staff, this possibility can be ruled out:
"The symbol just means the account has been closed, not necessarily for cheating or any one reason! The site no longer “calls out” cheaters so we aren’t going to have a cheat list or any other way to state “this person cheated”."
(cited by Gert-Jan in the forum topic "Gesloten accounts" in Dutch)
To add to the confusion, the account Cassini-Huygens initially did have an "account closed" symbol, but some days ago it disappeared.