Yes, it's true. If Buddhas and Enlightened Beings can degenerate, then there's no hope for us to attain ultimate freedom from samsara; and taking Refuge in the Three Jewels, as a gateway to the Path to Liberation and Enlightenment would hold no meaning.
I would like to point out that Kyabje Trijang Dorje Chang did not only give clear irrefutable reasons as to why Dorje Shugden is a Buddha(as above). In 'Music Delighting the Ocean of Protectors' he also says ordinary beings may not understand the ways of Enlightened Beings, through their emanations, like the Dalai Lama, an emanation of Avalokiteshvara. But their actions, ie Dorje Shugden's and the Dalai Lama's are "each as mutually universal and pervasive as the other" . As Enlightened Beings , their actions are motivated by great compassion. Seriously, as Trijang Rinpoche says, if Dorje Shugden were a spirit, " it is utterly impossible that such great beings who are special emanations of (e.g.) Arya Avalokiteshvara could lack the power to overcome the harmful force" of such a spirit.
Finally, Trijang Rinpoche also tells us that , "to the common view, it is difficult to fully understand the appearances of holy great Aryas and their inconceivable three secrets(body, speech and mind) at the definitive level". He then gives the example of Buddha Shakyamuni and Devadatta(who is supposed to be Lord of the Gods and will become Tathagata Devaraja limitless aeons from now).
Thus it is that,as Trijang Rinpoche has warned us, we should not be partisan in the seeming Dorje Shugden- Dalai Lama controversy. What may sound contradictory, as coming from the Dalai Lama, now, will be revealed as skilful means of a compassionate Enlightened Being in the future.