HIPAA does require direct written authorization from the patient for any disclosure which is not strictly related to the provision of medical treatment to the patient or in regard to payment for that medical treatment. So, your supervisors are correct, this does technically violate HIPAA, although it is a harmless violation.
You should ask that the lab technician sign a written authorization form for you (which you can download from the following page: http://www.aafp.org/fpm/2003/0200/p29.html)(or use the one that the clinic uses).
In regard to whether you can be fired for this infraction, this is compeltely within your employers discretion. The law is extremely favorable for employers. You are classified as an at-will employee
and may be terminated by your employer for any reason whatsoever, even if there is no cause. However, here, you have violated the HIPAA disclosure rules so there is cause for termination.
You will need to humbly explain to your supervisors that this was an innocent mistake and that you had not received any training regarding HIPAA but have gone out and educated yourself on it and understand it now and that this kind of disclosure will never happen again. You should also show them that you obtained a written consent for the disclosure and that there is no problem and no liability out there.
I would really be surprised if you were terminated for this, as it truly is a harmless infraction and you were just trying to help out the students.
Please let me know if you have any further questions. Please also kindly consider rating my answer positively so that I am compensated by the website for my work on your question. Rating positively does not cause an additional charge and does not prevent us from further discussing your questions.