Ask HN: Is it possible for a EU student to get an internship in the States?

I am a EU citizen studying in a university in the UK. Having seen plenty of posts here on HN about the stringent visa requirements, it left me wondering if it is possible for someone like me to get a summer internship in the States? I have been given the impression that it is feasible, but usually it involves too much paperwork to be desirable, especially with smaller start-ups. Leaving me wondering if it is actually doable?

Do I understand correctly, this case should fall under the J-1 Visa which requires a third-party (a sponsor) to monitor the intern? (this sounds rather off-putting from the company's perspective)

Any help or information is appreciated :)