Did someone send spam through my iinet mail account via my Mini Mac?

Question

I am very annoyed with iinet. They locked me out of my email account with no warning or explanation. All my important mail comes via that account and has done for 6 years. Imagine all the places that need to use my address to contact me - dozens and dozens.
I rang them and they claimed my email account and computer have been 'compromised'. I have a Mini Mac, 10.5.8 and a 2011 Macbook Pro. I use the Mail programme and my messages are deleted from the server immediately.
Is this even possible that my Mac has got a trojan? They have not sent me an iota of proof that spam was sent from my email account or my computer. But they claim their tech department traced the spam mail to my IP address. I just can't believe this.
Their solution is to make me change my password. As I believe the spammers are only spoofing - adding my email address to the 'sent' field - not hacking - I won't do it on principle. This is what iinet wrote. Please advise me how to respond because I am not changing my password if they are just being silly.
I understand that this is frustrating and a bit hard to understand. The processes involved with tracing issues like this are not easy and we have to stop all possible spam or compromises working its way through our network so no damage can be done.
Below is a basic outline of what happens:
1.            Operations Centre (OpCen) discovers spam or a compromise.
2.            OpCen trace the IP back to a username.
3.            The customer’s account is locked and active internet session terminated.
4.            OpCen create a PTS task outline the issue.
5.            CC contact the customer and confirm all threats have been removed.
6.            CC create an ETS work request (WR) advising the steps taken to prevent future incidents.
7.            The WR is reviewed and the customer’s account is unlocked by OpCen.
For whatever reason our OpCen team have traced your IP to your username and have followed our usual procedures to stop this from affecting our network.

Answer 1

Internet Service Providers needs to be forewarned, users frequently get spoofed about spam.  Shutting down their account due to suspected spam only weakens their reputation as an Internet Service Provider.
Spoofing can make legitimate e-mails look like spam simply by editing the reply-to address on your e-mail.
Sadly, spam e-mailers harvest legitimate e-mails by infecting various Windows machines and servers and grabbing addresses off their addressbooks.    People who mass e-mail you for legitimate purposes may actually be the harbingers of this problem because someone on their mass e-mail list may have the spam virus.  The way you can prevent it is:
1. Never publish your genuine e-mail on any website that doesn't securely hide it.  That includes Apple Support Communities postings.  You can edit your Apple Support Community preferences to hide your actual e-mail address in the profile (which I see you've done!).
2. When the recipient of a mass e-mail from a friend, tell them to only use BCC in their future mass e-mails.  
3. If sending mass e-mail yourself, do it only from an account you can afford to be bombarded by spam, or be spoofed.
4. Encourage the use of mailing lists that don't publish a person's e-mail, including social sites such as Facebook and LinkedIn.
5. Inform internet service providers that by setting up blacklists, they end up unintentionally making a file whih if compromised on an insecure machine, can backfire, and only create more spam.  Any internet provider blacklisting you is doing just that.