Sorry, but there is absolutely no New Testament Scripture that supports that sort of statement you made above. Please read the text:
LUKE !:1 Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,
2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;
3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,
4 That thou mightest know the certainty of those things, wherein thou hast been instructed
For sure Luke was a physician, and for sure Luke accompanied Paul on his missionary journeys; if otherwise then Luke could not have used the word translated "eyewitness" because then, he would be lying
Yours is an argument from silence. The only thing that silence proves about an issue is silence on that issue. The issue of "legal papers" is irrelevant because prisoners are never entrusted with their own legal papers, it is a common sense thing. Because Paul was accompanied by several Roman soldiers, and in the army, there are NCOs and officers to lead others, any legal papers would be entrusted to the leader of the group.
Look again at verse 4 of Luke 1 for the answer to the state of the salvation of Theophilus. I won't quibble about the date because its date is not important to me.