Error Logs about Email, but email works.

I was looking at my shared server error logs and found some related to my IP address. I had just made a change to my admin profile so I got sent an automatic alert email. This is what showed up in the error log:

[Mon Nov 26 10:58:05 2012] [error] [client my IP] 220-host364.hostmonster.com ESMTP Exim 4.76 #1 Mon, 26 Nov 2012

10:58:05 -0700
[Mon Nov 26 10:58:05 2012] [error] [client my IP 220-We do not authorize the use of this system to transport

unsolicited,
[Mon Nov 26 10:58:05 2012] [error] [client my IP] 220 and/or bulk e-mail.
[Mon Nov 26 10:58:05 2012] [error] [client my IP] 250-host364.hostmonster.com Hello localhost.localdomain

[127.0.0.1]
[Mon Nov 26 10:58:05 2012] [error] [client (my IP address)] 250-SIZE 52428800
[Mon Nov 26 10:58:05 2012] [error] 250-PIPELINING
[Mon Nov 26 10:58:05 2012] [error] 250-AUTH PLAIN LOGIN
[Mon Nov 26 10:58:05 2012] [error] 250-STARTTLS
[Mon Nov 26 10:58:05 2012] [error] 250 HELP
[Mon Nov 26 10:58:05 2012] [error] 250-host364.hostmonster.com Hello localhost [127.0.0.1]
[Mon Nov 26 10:58:05 2012] [error] 250-SIZE 52428800
[Mon Nov 26 10:58:05 2012] [error] 250-PIPELINING
[Mon Nov 26 10:58:05 2012] [error] 250-AUTH PLAIN LOGIN
[Mon Nov 26 10:58:05 2012] [error] 250-STARTTLS
[Mon Nov 26 10:58:05 2012] [error] 250 HELP
[Mon Nov 26 10:58:05 2012] [error] 250 OK
[Mon Nov 26 10:58:05 2012] [error] 550 No Such User Here

That (client my ip address) was on every line .
My email works fine.
My email is set to PHP.

The change I made was to my admin email - I changed it from a no-longer existent email to my yahoo email.

I asked my host what the error message might mean and the ever helpfull support desk sent me this back today:

Hello-

I looks as if someone is trying to use an email account to authenticate to the SMTP server that doesn't exist in the system.
I'm sorry, but I'm not sure what you are asking. Can you maybe rephrase your question or supply us with more detail about your problem?
How did we do? Please help us to improve the support that we offer you by filling out this online survey:

So, does anybody know what the error message might mean? Again - I got my alert emails fine. I tried the contact button and it works fine, and I know my order emails also work.

thanks
Joe

Just wanted to add - my host doesn't filter their error logs. When I go in to the cpanel and view the errors I see every single issue on the server, along with the IP address/URL of the site with the problem. To view my errors I have to pull up a random # (like the last 10,000 or 5,000 etc.) and then CTRL-F for my IP. It's a bit annoying, but I've had a good look now at everyone who is sharing the server with me. I just looked at the last 10K errors and I guess this email thing isn't just me or ZC - there are four other IP's getting the same error log on this server. So unless something jumps out at you, I'm not going to lose too much sleep over it.
thanks
Joe