The FAA will not write anything on the licence itself but may put details in your file. An investigation will be carried out by an FAA inspector who will write a report on the circumstances. This will be filed under AIDS which is on the FAA website. Link is:-
http://www.asias.faa.gov
Much depends on what is written on the report. If the report does not blame you then there is no problem. Employers may ask if you have had any accidents or incidents, just show them the report. If the report is unfavourable then you will have to either come clean and admit your mistake, or dare I say it, lie.....and hope that you are not found.
But, as you say, you were not to blame so there should be no need to hide anything.