Depends, Gourds can refer to several species. Bird House, Dipper etc are Lagenaria siceraria. Cultivars within this species will cross pollinate. The small colorful ornamental gourds ( Crown of Thorns, Egg, Apple ,Pear etc) are C.pepo. these will cross pollinate among themselves and with the summer squash and pumpkins. Loofa, Luffa cylindrica and Luffa acutangular only cross pollinate among their like species. Then you have Wax gourds (Benincasa hispida) and bitter gourds (Momordica charantia).
If he got good germination of the saved seeds, then the problem was probably the growing conditions. If poor germination, the seeds may have not fully matured before he harvested the gourd.