My husband claimed that the morning after pill would simply prevent ovulation - is this true?

No - implantation. The morning after pill prevents implantation by changing the hormone levels in the blood and thus in the uterine lining. The uterine lining (endometrium) must be ideal for the embryo to implant. Hormone pills (morning after and bcp) change the hormone levels that make the lining hostile to implantation. Hope this helps, best wishes.
No. That is true, but not the only reason the morning after pill works. There are effects on the uterus and the fallopian tubes, as well as sperm.