Well, actually, that is what the register says. Its heading is 'Births registered In.....', not 'Born In....'.
However, it helps to know what the law requires at the time you are interested in. From 1874 births had to be registered within 42 days or a fine was payable. So, you have to accept the inaccuracies of whatever records you are looking at. Sometimes there is corroboration, sometimes not, maybe baptismal records. But, in the end, if you won't or can't pay for certificates, you must accept a little inaccuracy.
Mostly, I accept that the exact date of birth or whatever it is, is not that important. More important is being sure that the record really is whichever ancestor you think it is. If the date is wrong by a month or so, so what, but the wrong person entirely is another thing.
Also, there are times when the certificate can open up lines of enquiry, with more data on parents, etc.