How Paul interpreted Scripture

In Acts 13, Paul and Barnabas are teaching in Pisidian Antioch, which is in present day Turkey (I think). Paul has an interesting moment in his sermon where he interprets Psalm 16:10, which says 'You will not let your Holy One see decay.'

Originally, this Psalm appears to be written by David while he flees Saul's persecution, and it seems like the natural, original interpretation would have been that David believed God wouldn't let Saul kill him.

However, in Acts, Paul puts a different spin on it. He notes that despite this verse, David did in fact die, and presumably decay. But having come to believe in the Gospel, Paul argues that Psalm 16:10 in fact refers to the resurrected Christ, who in fact, unlike David, did not decay because of his resurrection.

I can imagine an interesting thought process behind this. I can imagine a younger Paul (Saul) sitting in his Bible classes reading Psalm 16:10 and asking Gamaliel (a famous rabbi Paul is said to have learned from) "yeah, but didn't David actually decay? So what does this psalm mean?" and I can imagine Gamaliel responding, "well, here decay actually means death at the hands of Saul." Maybe Paul accepts this at the time as the only logical interpretation; maybe he thinks 'well, that's an odd way to write the verse, but okay...'

But then years later after Paul comes to believe in the Gospel, he says, "Oh, now I get what Psalm 16:10 really meant: it refers to the resurrected Jesus Christ."

A recent post suggested that often Scripture doesn't err, but we err in our understanding it. That's probably right. I'm also encouraged by Paul's reinterpretation of the Psalm because sometimes I read the Psalms and Scripture generally and wonder if I completely believe what's being said. For example, Psalm 103 describes God as one "who heals all your diseases." But if I read this to simply mean God restores bodily health, I don't fully believe it because while sometimes that's arguably true, other times it's demonstrably false. So in what way is this true? Well, I'm not sure--but I wouldn't be surprised if the answer came from the same place as Paul's interpretation of Psalm 16:10: God heals all our diseases in the resurrected Christ.

So, I'm encouraged both by the possibility that there are greater and stunningly literal interpretations of Scripture that I may one day learn, and also by the notion that all the Scripture is fulfilled in Christ.