she's said she doesn't feel 'safe' around me...so why so eager and willing to be within a foot of me?
That alone is reason to be keeping your distance. Who knows what she might say or accuse you of after working wth you? Has the study coordinator - who you say you normally never deal with - been influenced by her to try and get you on the scheme?
Seems strange that, knowing your history with her, management seem happy for you both to work together.
Hope you can find out what's behind this - seems a little fishy to me.