They don't claim; they are. Merlin are the second largest operator of entertainment attractions in the world, in terms of visitor numbers, locations and revenue. Size means bugger all though.
The UK, as an example, is the fifth largest economy in the world, but has the highest rate of homelessness in the developed world (
https://www.ft.com/content/24117a03-37c2-424a-97ed-6a5292f9e92e)
Being the largest, or second largest, company in an area doesn't necessarily mean that your quality values, or levels, are the highest. It doesn't mean you're the best operator. It doesn't mean you're the best thing since sliced bread. It just means you have the most custom.