"You have one shot at curing this, and should give it your best" is a generalized statement, factual, and meant to alert, that after your initial treatment with surgery, chemo and radiation or whatever treatment combination you have, if there is a recurrence, it is more difficult to treat the 2nd time around for many reasons, and sometime it may not be treatable, but each cancer is different, so is the location, involvement, TNM staging, initial treatment, the patient, age, health, as well as the doctor's experience, and many other factors, that are taken into consideration, so it's not directed at any individual, and no one has a crystal ball, not even the doctors, but that everyone should consider all treatment options offered, and available to them, sometimes even at another institution, and to put your heart into it like your life depended in it! Most CCC consider the guidelines by the NCCN, have up-to-date treatments, top doctors, training, but everywhere else, I'm not too sure, and each patient is a co-contributor to his or her own health care, not just the doctors.
There are many here who have had more than one recurrences, and were treated successfully, including myself 5x. If I could go back, would I change some aspects, yes, but I did not have this or any other sight to go to to see what others have done, and suggest. I just post to try to help others with my experience or lack of experience, mistakes I made, and share information I gathered for the past three years, and I've been to hell and back.
Anyway, if chemo was not offered to you, your doctors probably felt it was not necessary, and treatable with Surgery and Radiation alone, which is the only thing that cures HNSCC. I see you went to UCSF, which has one of the best ENT programs in the country, and can be assured you received the best care. You are two years out of treatment, and most recurrences occur within the first year.
In hope this answers your question, be well.