Say Tehilim or Learn Torah?

A certain merchant from Metz would earn his living by selling furs, primarily at the seasonal market fair in Vilna. Everyday this merchant, who knew how to learn a little, would finish selling for the day and go the beis midrash of the Vilna Gaon and say Tehillim.
The Gaon noticed that he was no ignoramus and was a bit perplexed as to why he said Tehillim instead of using his time to learn. He decided to ask him why.
The merchant replied, “I do this because of something I heard from our Rav in Metz, Rav Yonasan Eibeschitz, zt”l. He taught from our sages that Dovid Hamelech asked Hashem that Tehillim should be considered like learning the hardest areas of Torah. Surely we see from this the greatness of Tehilim since Hashem certainly did not refuse Dovid Hamelech.”
“But why do you think that Hashem would not refuse Dovid Hamelech?” countered the Gaon. “In Bava Basra 17 we find that the gemara entertains the possibility that Hashem did refuse Dovid a request. There we see that the gemara entertains the possibility that Dovid was one of the very few whom the worms could not overcome after death. One opinion cites Dovid’s prayer in Tehillim 16 where he pleads that his flesh be protected from worms. The other opinion disregards this proof out of hand since this was merely what Dovid asked for, not what he got. Please ask your Rav how he answers this question which seems to show clearly that a request of Dovid’s may not have been accepted?”
The next year, the merchant was back and sure enough he had an answer from Rav Yonasan. “My Rav said that that is not how he learned the gemara at all. The opinion that says that this was merely prayer does not mean that Dovid was not protected from the worms. He requested this in Tehillim and surely it was granted. This opinion merely posits that Dovid should not be included in the list of those who were protected because of their righteousness since Dovid was merely protected because of his prayers, not because he deserved it as a result of his personal purity. Similarly, no one would really believe that Dovid requested something from Hashem which he did not receive without a clear proof that he was not answered. Since we see no indication that Dovid was not answered you may definitely continue to say Tehillim in the beis midrash, and have it considered Torah study.”