Does it matter? Does it matter who wrote Hebrews? It has not mattered thus far. What matters is that the Church has declared it to be Canon.
Well, the Church did much more than declare Hebrews as part of the New Testament canon. At the Council of Trent, they said this:
I know what they said; and at the time to the best of their knowledge, they attributed Hebrews to Paul. It is to the credit of the Church that they acknowledge that Pauline authorship is rather farfetched. The Church knows better today. How about you?
How could the "Church" know better today, rather than closer to the actual genesis of the epistles when Paul was considered as the true author and was acknowledged by church theologians within the first century? And, are you finally admitting that the "infallible" Magesterium that comprised the infallible articles of the Council of Trent were not all that infallible? Quite an admission on your part.