Have you ever met someone who is really pushy and won't take "no" for an answer. I find people like that really unpleasant and sometimes creepy and even scary.
It's probably the same for your dog. The other spaniel wouldn't take no for an answer. The appropriate response from him when your dog sought safety with you, would be to back off and give her room to get comfortable and come out of her own accord.
I see my dog at both ends of this play initiation. If the other dog looks unhappy - despite initiating play - she backs off, or I call her off. And then the other dog is often reassured and comes out to play again more happily. Or they don't. It's not something that pushing hard (eg by the male spaniel) will help. The pushy dog must back off or the insecure dog will never feel comfortable.
If my dog ends up with me for security, it's almost always because the other dog plays too rough for her and won't lighten up. So I will defend her against that kind of dog. My dog on the other hand, matches exactly the kind of play the other dog is up for. Nothing with scaredy dogs. Lick on the chin for old dogs, and wild games of bitey face and chasey with other farm dog bitsas. And run away and hide from dogs with really thick coats that bite too hard.