I've worked with and hired people on H1B. At least from my experience they're treated (from a job offer perspective) just like any other candidate. Some get bigger offers because they negotiate well, are in high demand positions etc and some don't. There was no lowballing candidates because they're on H1B or need sponsorship.
Then that's your experience. I've worked with H-1B where their salary was lowballed or job title was. Not to mention the difficulty in switching jobs and 5 years in, they were severely underpaid.
My original comment about being two faced I still stand by.
