The caretaker is incorrect. People often cut the seed heads off daffodils so the plant's energy goes into making a strong bulb for next year instead of seeds in the seed pod. If you don't do this it only makes a tiny difference, so don't stress about it if you miss them.

According to this website -
http://www.blog.allaboutdaffodils.com/2009/04/blind-daffodils-what-causes-them-to.html
blind daffs are due to being planted too shallowly, getting too much nitrogen, viruses, being overcrowded or plain old pernicketyness.

What a brilliant answer, Beattie!

Cutting the flower stems with spent heads on top won't affect next year's flowering - cutting off the leaves before six weeks after end of flowering will be very detrimental to the bulb and most likely cause 'blindness'.

I have made sure that I do not cut off the foliage, and I will let it die down before removing.

I thought it was incorrect, but I wanted to make sure.

Thanks for the advice. It is much appreciated.