Hi Beth, I read somewhere that the vast majority of people obtain their PhDs after a resubmission.
I read your post last night before I went to bed and ended up having nightmares about receiving the same sort of letter from my university! I think your supervisors are right, they could have failed you at the viva, but they saw merit enough in your work to award you with a PhD subject to meeting their corrections etc. Examiners want us to pass!
I have until August before I need to submit my thesis again, but I just wanted to wish you the best of luck.