"It's a well known company.... experience..."
If it's that well-known of a company, it's probably run by executives using the same bait and switch / exploitative employment tactics as others like facbeook, google, microsoft at this point, etc.
don't mislead yourself into taking a position for the experience.
A job at Microsoft is still just a job, and you'll be huddled up in a cube the same as any other.
In reality, you should examine your feeling that you can accept less wages to work at this company solely because of their brand, as this is the result of a very complex marketing campaign lead by this and other companies.
Oh, you're going to be working here! Do it for the glory! Do it for the fame! Do it for anything but the money.
It takes less money to pay media outlets to glorify your company, persistently, over the years, than it does to pay good wages to thousands of employees. So stories like this one are very common among applicants of well known organizations. They have thousands of slots to fill.... If they can shave even 1%,3%,15% off the salaries of 1000 people coming in.... that adds up to a ton of money, that they can use to create other positions.
In short, I doubt they mistook your 4 years of experience for 7. They might have a shady recruiter that did this because they wanted commission, but the hiring manager would have seen your resume, and HR probably did too when they made the offer, if it was so dependent on experience.
Something I've realized over the years, and this is more of a concept in other countries than the US, but is becoming more common, is that some people will negotiate until the very end. It doesn't matter what they're saying when they're coming back to you with this - it's a negotiating tactic.
If they were able to offer you that money "at 7 years experience", then you know they have the budget for that much money for that position. End of story. I would say you're willing to accept at that originally offered rate, otherwise you will continue looking elsewhere. Do not accept anything else, they will likely either cave, or it will be a position where other shady things will have happened later on and you can be glad you didn't let yourself get taken advantage of by management BEFORE EVEN STARTING THE JOB.
Imagine the mind games that would follow later on.
^ Additionally, this may be a filtering technique. Maybe they're only wanting to hire people they can manipulate like this.
And depending on the amount of the change... Say it's $5k/year. Maybe $10k/year. A company should be able to overlook that slip up anyways. It's an amount of money that, when looking at a department level, etc, is more or less a rounding error.
A company wouldn't throw away a good candidate because of a mistake they made when hiring them. Not a good one anyways. I could see perhaps them doing it if they had concerns about someone making more than someone of the opposite sex with the same qualifications.... but even then. I think you should avoid this company.
The amount they pay the recruiter that found you for this organization, for example, is likely above $20,000, (or perhaps 20-25% of the salary for the position). So quibbling over small amounts (really, anything under ~10k / year or so) would seem petty on their part