perhaps they called to check with the council. I had a property for which i was paying 75%, then when i moved in with Mr CRX i was staying here for 5 days a week and with my mum for 2 days. The council said that Mr CRX could still get his 25% discount as i was also paying elsewhere. They would rather have 150% than 100% i suppose.
There is more than one type of council tax discount. A house full of full time students is not liable for any council tax.
A severely mentally ill person does not count.
why would you want to check what they're claiming? its not your business to know what they are or are not paying - if you believe they're committing fraud, then report them and the council will do the checking.