I was called into my director's office on 12/10. She told me I had accessed a patients chart on the lab queue two times in the same day. Just in and out, did I know why? This had happened two weeks prior and I did not remember. Mistakes are made everyday by transposing numbers, a chart is coded and doesn't get completed out by the coder, etc. Bottom line, I did not intentionally do anything wrong. I was not terminated for this accusation until a week later. If I was such a risk, why was I allowed to work another week? Any advice would be helpful.

First is policy. If policy is clearly stated that 'more than once in 24 hours is automatic termination,' then that's that.
Second is the whole story. There could be nuances we know nothing about - your history, the type of lab work, the sensitivity of the patient's condition, your relationship with the patient (was it your patient, a friend or relative, someone you know, were you supposed to be accessing that chart the first time?), on and on. You don't even say what your job was.

Unintentional means basically nothing in the medical field (or most of the workplace).
Your question about why you were allowed to work another week is also not meaningful. You were possibly monitored very carefully while meetings were had behind your back.

And often it takes time, in some terminations for staff members to meet, discussion and a decision on what to do.

Also you were fired for violations, they assumed and decided were real, (not alleged)

Most of the US is at will employment which means you can be fired at any time for no reason. You are asking questions we can't answer because we don't know the other side. We don't know what rules govern your employer or employment. We don't know what other circumstances were involved like did the patient make a complaint, was info leaked, etc.

Your employer might have recently been fined for HIPAA violations and they are very sensitive to them.

Your questions should have been discussed during your exit interview.

It wasn't an alleged violation, it was a real violation detected by a time stamp on the EMR (electronic medical record). These time stamps tell who accessed the record, what time the record was accessed, and how long it was accessed for. Due to the sensitive nature of the medical record, HIPAA is taken very seriously. With the changeover from paper to computer it is easier to determine who accessed the record, therefore, we in the medical community are held at a very high standard and simple mistakes involving HIPAA are taken very seriously and dealt with accordingly.

You you say it happened 2 weeks before and you couldn't remember. Had you remembered, and had a logical explanation, the outcome might have been different. But, rather, you had no explanation, so it appeared to your superiors that you were covering something up. Your employer has to answer to all violations, if they cannot provide a reason why that record was accessed by you, or other employees not involved in that patient's care, they get fined and may be denied payment for that patient by the insurance company, especially if it is Medicaid or Medicare.

Your next question refers to why it took so long to be found and brought to your attention. Chart reviews are only done by a select few people in the facility. They cannot reasonably review every chart on every patient in the span of only a few short days. Chart reviews can take weeks to months to complete.

Chart reviews are also done by the insurer of the patient. The insurer has the right, and the ability, to know of every person involved in the care of said patient. If you were not directly involved, i.e. laboratory, radiology, pharmacy, nursing, case management, etc. then you had no right or reason to access that record.

To reiterate, had you had a reasonable explanation for accessing the record, the outcome may have been different. Since you had no reasonable explanation, other than mixing up numbers, or something similar, that sounds more like an excuse than an explanation.

I'm very sorry this happened to you, especially this time of year, but take it as a learning experience and be more careful in the future.