Quads two days apart, really?

This is a report from the The Gentleman's Magazine: and Historical Chronicle. From January to June, 1814.

"1814 -March 4. The wife of Mr. James Pickworth, grazier, of Sempringham, Lincolnshire, delivered of two boys, after which she was so much composed, that she got up the next day, and remained in that state till the 6th, when she was delivered. of two more boys!"

Could this be true? It is difficult to know after two hundred years, but I have done some investigating and found the following.

Baptisms:

James Pickworth 5 March 1814
Thomas Pickworth 5 March 1814
William Pickworth 6 March 1814
Robert Pickworth 6 March 1814

Baptised at Sempringham, parents James and Anne Pickworth

Sad to write all 4 children were buried on 10th March 1814 at Billingborough.

James Pickworth 4 days old
Thomas Pickworth 4 days old
William Pickworth 4 days old
Robert Pickworth 4 days old

Therefore Anne did give birth to four children on two separate days, but the result was not as James and Anne would have liked.