Luke doesn't claim he was "divinely inspired". He claims in Luke 1:3 that he just wrote down stories as told to him by sources he didn't specifically identify. The "Christians" you are "familiar with", probably think that Luke was an associate of Paul, and therefore Paul was probably a probable source for Luke, and they probably think that Luke wrote Acts. Their beliefs are speculation most probably based on their indoctrination by the daughters of Babylon (their churches).
Their "divinely inspired" reference probably comes from a letter written by Paul to Timothy, whereas Paul was actually speaking about the writings he had from youth, which would be a referral to the old testament writings and not the uncompiled and mostly unwritten NT writings Calling something "holy"/divinely inspired without proper investigation is known as a snare, which will often catch someone and take them were they would rather not be. What false prophets claim, or even their followers claim, has to be taken with a grain of salt. The blind following the blind generally winds up with both parties falling into a hole.(Mt 15:14)
New American Standard Bible Proverbs 20:25
It is a trap for a man to say rashly, "It is holy!" And after the vows to make inquiry.
Matthew 15:14 Leave them; they are blind guides. If the
blind lead
the blind, both will fall into a pit."