Can an employer hold me to the terms of an Employment Letter, but break the terms himself without penalty?

In my specific Employment letter, a clause states that: "...However, due to the nature of your position, and to ensure client continuity, you are requested to give (1) one month notice before resigning from your position. Should (company) need to terminate your employment, you will be given (1) month notice, or payment thereof in lieu of notice. In his email reply to my 1 month resignation letter, the President wrote: 3. Timing of release from employment: a. (company) may be able to release you earlier than 30 day notice period, subject to successful transition as determined by x and x. Once x and x signs-off on transition, HR will start the off boarding process and will determine last date of employment based on time needed to complete off-boarding process. (company) will meet its obligations per employment agreement in place, in regard to notice period payment if any." After I finished these tasks, I was told that the company could release me without paying the month