One of the problems is you may not be legally entitled to purchase or posses a firearm from a Federal level, but may be eligible for a CHL because the crime is no longer a felony in Texas, but a misdemeanor. This is one of the weird changes that was made.
If what you stole was less than $1500, and not one of the other items listed:
then this may apply:TPC 31.03
(3) a Class A misdemeanor if the value of the property stolen is $500 or more but less than $1,500;
(4) a state jail felony if:
(A) the value of the property stolen is $1,500 or more but less than $20,000, or the property is less than 10 head of sheep, swine, or goats or any part thereof under the value of $20,000;
(B) regardless of value, the property is stolen from the person of another or from a human corpse or grave, including property that is a military grave marker;
(C) the property stolen is a firearm, as defined by Section 46.01;
(D) the value of the property stolen is less than $1,500 and the defendant has been previously convicted two or more times of any grade of theft;
(E) the property stolen is an official ballot or official carrier envelope for an election; or
(F) the value of the property stolen is less than $20,000 and the property stolen is:(i) aluminum;(ii) bronze;(iii) copper; or(iv) brass;
So, if you meet the guidelines for a misdemaor now, and the NICS was an error, you should be eligble no matter. You would still have to declare your conviction, but the DPS shoudl see it no longer fits the felony status of a crime.GC §411.172. ELIGIBILITY.
(b-1) An offense is not considered a felony for purposes of Subsection (b) if, at the time of a person's application for a license to carry a concealed handgun, the offense:
(1) is not designated by a law of this state as a felony; and
(2) does not contain all the elements of any offense designated by a law of this state as a felony.