but didn't he say that if an idea, such as wisdom, is strong enough, then a new spirit can be born, but it won't be the same as the original spirit?
Yes, his statement (which can be correct or incorrect) is that if the spirit is strong enough then some part of it could still remain and exist in the part of the Fade where the original spirit dwelled, but it would likely not remember Solas.
But even if this is the case, I think the Forbidden Ones are on a completely different level than Solas' friend, or even Cole. The Forbidden Ones are ancient spirits who have existed for millennia, and they have picked up much knowledge and magic in that time. So even if they are killed in the physical world, their spirits may just slip back into the Fade without any adverse effects.
I think the only thing that can actually destroy spirits like that is being killed in the Fade.
In fact, I think Origins states somewhere that demons slain in the real world simply return to the Fade unscathed.
Cole also has a banter with Vivienne where she asks if it angers him to see his demon brethren banished back to the Fade, and he says he is happy for them because they don't hurt any more since they are now back where they belong. So that sort of implies that they retained what they were.