The words "may be eligible" would stop me cold. That is not something I'd bank on in this case, because there is already the review they can whip out if they challenge the unemployment reason, and that shows that prior to you being treated at this time, you were not doing the job as required.

Be very careful with this. At the very least they will challenge the claim and they are probably going to win due to the documentation they already have (review). Then you'll be out of a job and no unemployment.