Was Jesus an adherent to 'Sola Scriptura'? Adherents to Sola Scriptura basically believe that Scripture should be the foundation of all doctrine.  (NOTE: That is not to say that outside sources cannot be used to aide us in understanding the text - see here.)

Based on what we know about Jesus from Scripture, could Jesus be considered an adherent to this philosophy?
The answer is simply: No.
One way to prove it, is to take the verse where Jesus says:

"Whoever listens to you listens to me. Whoever rejects you rejects me. And whoever rejects me rejects the one who sent me." (Luke 10:16)

That means, that whatever the apostles say, is Jesus' teaching. Then we can take Paul's words to the Thessalonians in chapter 2 verse 15:

"So then, brothers, stand firm and hold to the teachings we passed on to you, whether by word of mouth or by letter." (NIV)

This is saying to hold to the scriptures and oral teaching. One link that might prove helpful is here, asking: "Sola Scriptura vs. the Magisterium: What did Jesus Teach?". One that deals with just Sola Scriptura can be found here.

One link that might have an answer, says:

Did not Jesus say, "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. . . ." [Matthew 28:19] Of course this admonishes them to teach; it says nothing about writing. And the Bible itself says nothing about it being the sole source of God’s revelation.

Anyways, that is just my opinion and it may be a little biased. One thing to think about, is that for the first couple hundred years, there was no "New Testament". The last of the gospels by John, was written by A.D 85 or later. 

I agree with you that:

If a person teaches something contrary to Scripture, they are wrong.

But sometimes things may seem contrary and actually be true to each-other. Here is a link that explains some things that seem to contradict each-other in the bible, but just need a little explanation (I know that that is both sources from the bible, but it is basically the same).

And just to let you know, I'm not Roman Catholic.