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From what others have said, any and all filtering doesn't occur until you log into your SpamCop e-mail account ... this is based on folks complaining of login issues, timeouts, etc. ... symptoms of a SpamCop e-mail folder being too full ...
Wazoo: I know you don't use the email side of things. To correct your information on this... There are 2 types of filtering (like 2 different Held Mail locations. Confusing, isn't it?).
The first are the filters that use the bl.spamcop.net and the other dnsbl's along with SpamAssasin and this filtering happens automatically if enabled, even if the mail is then forwarded to another server. To enable it, log into webmail, select Options, SpamCop Tools, Select your email filtering blacklists. Check the dnsbl's and SpamAssasin settings you want and/or the Block All or Tag Only switches as wanted.
The second filters are for moving messages around while in webmail and those only work when you are logged into the webmail application. You can do things like discard all of the spamcop confirmations or move all of the message from Aunt Linda to the inbox (after whitelisting her address). You can access these filters by a Filters button at the top of the page or Options, Filters.