@axpert,
Pretty much your friend is right. Obviously this person either has the following "trinity":
1) Lying about her true feelings and doesn't want a relationship with you but is afraid to hurt your feelings by telling you (assuming that she wants to appear empathetic given your tumor situation).
2) Has someone else on the side but wants her cake by stringing you along in case that relationship doesn't work out.
3) Is telling the truth and coincidentally the times are just bad and is she could be sincerely sickly.
But more likely than not she is most likely playing games and is dishonest about her feelings and is not respecting yours by her own dishonesty (assuming she is dishonest to begin with).