If this is the trainer's first offense, and has an otherwise good employment record, I do not believe they should be fired, as long as they handle the situation properly.

First, take responsibility for the screw-up. Don't make excuses for why it happened, accept that it did and do whatever can be done to fix it.
Second, go out of your way to make up for it. For example, if the store says you need to write an apology to each person in the class, take it further. Call each person individually, apoloigize and try to offer what you can to make it up to them. Then follow up witha note...a hand written note, not a form letter.

It is a big screw-up, but we are all human and mistakes happen. I think it is more important how we handle our mistakes and what we do to fix them.