score:6
You have received conflicting information from two sources...
They both cannot be right. And the answer is that the customer services email (Hinduja) is wrong. The web site is correct. This is to say that the rule governing long-term visit visas is...
You can stay for a maximum of 6 months on each visit.
That means you can stay for 6 months, take the ferry to Calais, and return for another 6 months back-to-back. The rules state that a visitor can stay for up to 6 months on each visit.
The rationale is that it normalizes visitors with non-visa nationals (e.g., Americans, Canadians, Aussies, etc), who can also stay for up to 6 months per visit without a visa.
NOTE: there is a deeply entrenched internet myth that a visitor can stay for 6 months in a rolling year. It's wrong, there's no such rule. But the myth persists, and we can see that even UKVI's customer service has fallen victim. It's always worse when people get something 'official' that's wrong and then vector it on the net as 'official'. There's a related article here.
NOTE: The rule itself is stated here.
If you can prove you need to visit the UK regularly over a longer period, you can apply for a visa that lasts 1, 2, 5 or 10 years. You can stay for a maximum of 6 months on each visit
NOTE: Finally, take note that these visas are hard to get. You need to be an end-user for a long time before you can qualify, and then you need to have an airtight reason.