Employment Law Questions? Ask an Employment Lawyer.
Good evening and thank you for entrusting me to assist you. I am sorry to hear about this scheduling confusion. If you would please, can you clarify what your specific question is?
I'm afraid to say the answer to that question is most likely "yes." The reason is because employment in the state of NY is "at will" absent an express agreement to the contrary. At will employment can be terminated (and by extension, simply modified) for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination or modificatio is fair, reasonable or even true.
Thus, an employer could lawfully discipline or even terminate an employee due to a scheduling misunderstanding such as what you describe. Now, just because someone can legally do something doesnn't mean that it is in their best interest to or that they will. Here, your confusion was completely understandable, and any employer who disciplined you for it would just be shooting themselves in the foot. It would not be illegal, but it would be very bad management.
I hope this helps. If I can clarify anything at all for you, please do not hesitate to ask. It is my pleasure to assist you further if necessary....