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Tell them to send you the proof - otherwise, you have no way of knowing what hole they are referring to. The problem here is this, they know that it happened, and maybe it acutally happened. Within the hosting environment, that means they either have some foms of trip wire running, mod_security, or snort. So, they should have the specific POST payload driven to execute.
More than likely - and I am taking a big guess - they uploaded something to the /tmp directory of the server. /tmp could be anything, so it's an example here. They then tried to execute the script. Since they (hosting company) saw it come through that specific file, they saw the specific command.
Here's what bothers me, and I am a PLESK reseller, it sounds to me that they DON'T have all of the security measures in place, and that the script was executed - probably a mailer of some sort. If youare on a Virtuosso (VPS) environment, it may also be a problem where the "script-kiddies" know the script is already on the physical server, and they are just trying to exploit it through a known PHP script that may give access to the /tmp directory.
This is probably more than you need to know, but it always bugs me that "hosting" companies tell you there was a problem, but give no proof or details...good luck!