Well, reading his reply to her, he's rude and has no social as, but what he said wasn't inaccurate. What he should have done was tried to sell her private one-on-one training first. The dude is just guilty of being rude and having no tact, which won't serve him well as a trainer in a "corporate gym", but at least he said it via msg, not face to face.
This lady chose to make the "conversation" public and further embarrass herself.
I see this as a no-contest. Both people lose. She got her feelings hurt and suffered no monetary damages, however she goes public with it with the intent on inflicting monetary damages on him. If I were him, I'd sue her, however lawsuits are handled differently in the UK, not to mention it's a socialist country full of whining social justice warriors who would probably side with the obese crybaby.