It's missing a comma and/or em dash.

"I could not get past your first level support, who -- and I do mean this harshly -- sounded like they didn't pass first year business school."

I understand the sentence. What I don't understand is why it is necessary for a support agent to have completed first year business school and why this is an insult (which I take as the intent).

My guess is that they were talking to some kind of business support (as opposed to technical support), and it's a way of saying "they didn't know what they were talking about", when the reality was probably "I want to do something that their company doesn't want to support, and I'm upset that they didn't buy my argument".

They mentioned being a "case that falls outside [Stripe's] remit", and that Stripe didn't "give them the benefit of the doubt".

Ah, that wasn't clear and punctuation was the most glaring issue with the sentence. Nevermind!