I would like to re-train the Stanford NER library from scratch as a 1 class model.
Only 3,4 and 7 class models are available out of the box.
Is it possible to obtain the data that the model was originally trained on?
The original paper mentions two corpora: CoNLL 2003 (apparently here now) and the "CMU Seminar Announcements Task". However according to the page linked in the question the actual NER was trained on a larger combination of corpora:
Our big English NER models were trained on a mixture of CoNLL, MUC-6, MUC-7 and ACE named entity corpora, and as a result the models are fairly robust across domains.
So it might be difficult to obtain the exact original training data. However most of these corpora were compiled for some shared tasks and should be available online. There are probably more recent ones as well: a quick search "named entity recognition shared task" returns many hits.