The 1961 film of The Innocents ,directed by Jack Clayton, gave a stronger suggestion that the ghosts did exist, than did the 1898 novella, Turn of the Screw, written by Henry James. There is some dispute as to whether or not Miss Giddens was going crazy. I found a problem with that view.
In the film when Miss Giddens (Deborah Kerr) first arrived at Bly, she thought she heard someone calling Flora's (Pamela Franklin) name. This was a little too soon for Miss Giddens to be losing her mind. Mrs. Grose (Megs Jenkins) said she had not been calling for Flora. Miss Giddens was also wandering near the pond when she heard this. The pond could have been considered Miss Jessel's (Clytie Jessop) place to haunt since in the film Miss Jessel had died by drowning herself in the pond. The film also makes the point that both Miss Jessel and Peter Quint (Peter Wyngarde) had died at Bly, whereas they had died elsewhere in the novella. Many people believe that if someone, who had been treated unjustly or has some unfinished business on earth, dies at a certain place, then his or her spirit cannot rest and may continue to haunt that place.
There are also more clues that hint the children may be at least aware of the ghosts. Miles (Martin Stephens) was linked to each of them by finding Quint dead and possibly seeing a hand, possibly Miss Jessel's, in the pond. Flora also discussed death with Miss Giddens. She asked if some people were left to walk around on the earth. This could suggest that maybe she has seen the ghost of Miss Jessel. The children also ask about keeping secrets. The children could have pushed Miss Giddens to lose her mind; whether they were aware of the ghosts or whether the ghosts were somehow conspiring to use the children as pawns.
The film also shows a very clear vision of the ghosts through Miss Giddens' view. Because we see and hear evidence of their existence ourselves as they haunt the estate, the governess, and the children, this makes it easier to imagine the ghosts being right there at Bly.