Advice needed on IRS appeal

I have an interesting issue regarding a 2009 timely-filed 1040. IRS came back with a CP-2000 showing unreported income. TP responded to CP-2000 in late 2013 (no 30-day notce) by submitting disagreement response along with an amended return to document extensive changes to original return and disagreements with CP-2000 calculation of liability. Net result of TP changes was an increase in liability from original 1040 (though less than IRS was seeking). In April 2014, IRS calculated interest and penalties due on the TP-calculated additional liability and TP paid full balance. TP has paid all past tax liabilities and is current on all tax matters (not that this should matter). TP just received a 105C letter disallowing a "claim" for $9K on the 2009 return because the 1040X was not filed timely. The $9K appears to be related to the difference between the CP-2000 calculation and the liability proposed by the TP in the response to the CP-2000. I spent an hour this morning at the local IRS office determining that 2009 has not been closed out even though it is currently showing $0 balance. The local agent thinks that the CP-2000 response was processed as a stand-alone 1040X and that why it's now being disallowed as untimely. Her suggestion was to file an appeal to the 105C letter following the directions provided in that letter. Does anyone disagree with this advice? If so, what should be done? As of today, the IRS has not requested payment of any amount (though it's possible [likely?] that there will be a notice soon requesting payment of the disallowed "claim"). As a thought exercise - even if the issues raised by the TP in the response to the CP-2000 were disallowed as not timely filed, if the TP pays additional amounts towards 2009 liabilities, wouldn't those amounts be open to a refund claim filed within two years of payment? Ira Smilovitz