It isn't true in all cases obviously, (I hope that satisfy's the 'shared parenters' amongst those reading this post). I'm a campaigner who would be satisfied with stronger protection for contact/access rights than provided by the balance of the child's best interests test.
I imagine your ex. managed to persuade the courts that your children's interests were best served by staying with him originally, so you should how difficult it can be to defend yourself from those arguments. You may never know your ex.'s real reasons for his change of heart, and you clearly don't feel all that convinced by the one's he's given you (why should you - do you think I believe a word my ex. said - she was an alienator who claimed to have had absolutely no influence on our daughter when she refused contact with me).
I wish you good luck, you clearly have plenty of heart for the job facing you now.
ATB, Graham