The State Pension is a weekly benefit, paid in multiples of a week. For people who reached State Pension age before 6 April 2010, it can be paid weekly in advance or four weekly in arrears.
For people reaching State Pension age on or after 6 April 2010, a payday is allocated according to the final two digits of the customer’s National Insurance number. Payment is weekly, fortnightly or four-weekly in arrears. State Pension payment arrangements
This government document does not mention 'monthly' anywhere. I can only think that those, who think that is how they are getting it, are well off enough not to notice the change of date each month.