Are the records of incoming call numbers  to cell phone which can be
purchased on the internet but are not on the monthly statement
accurate?

Im unsure for the states but in Canada incoming calls are not listed
on the statement. If you can view them online I would assume they are
accurate provided they are from your cellular service provider and not
another company.

Well in the US, Your incomming calls are listed on your statement, i
dont know of a servece that lets you look at a statement online,
althou i havent look at them all.

I have T-Mobile and can view my statement online, it's very current,
nearly to the minute.  I live in the US.