Confirmation of the rep's story comes directly from Korean manufacturer LG. On the LG website is an updated User's Guide for the LG Spectrum and on the guide is some references to Ice Cream Sandwich and the features that come with the update such as multi-tasking. Updating the Guide would seem to indicate that LG has done its part. It would be great if we had some idea of when to expect Android 4.0 on the LG Spectrum, but as we know, carriers are a mostly unreliable lot when it comes to pin-pointing an exact date for anything except when a customer's monthly invoice is due and when you're entitled to upgrade your current phone.
source: LG via AndroidForums