Right. This is where my "...In talking to my lawyer, he thinks..." comment comes in. Sometimes just the threat of a messy legal action is enough for them to pay up.
Six months salary is much cheaper/easier/cleaner than going through a legal battle. A company with 7000 employees should make that calculation pretty quickly.
My best friend went through this just last year. They made a few counter offers but ended up in court; he ended up with 2 years pay and benefits.
In my BIL's case, (after 20 years, his performance was suddenly sub-par at age 60) he just said "Do I have to talk to my lawyer about this?!" and all the dogs were called off.
When mgr asks what appointment I have, I tell them its with my lawyer.