There are a number of reasons why he might have been denied. If he tried to hide his arrest, he'd be denied because of his dishonesty. If he admitted guilt at any point, or entered a no contest plea to enter that diversion program, it would be a conviction under 101(a)(48)(A). And also, the difference between my case and his is that theft doesn't display good moral character. And while one might say violation of laws relating to controlled substance laws generally doesn't display good moral character either, Act 101(f)(3) states that a single offense of simple possession of up to 30g of marijuana is an exception.

Sources:

101(a)(48)(A):

(A)The term "conviction" means, with respect to an alien, a formal judgment of guilt of the alien entered by a court or, if adjudication of guilt has been withheld, where-

(i) a judge or jury has found the alien guilty or the alien has entered a plea of guilty or nolo contendere or has admitted sufficient facts to warrant a finding of guilt, and

(ii) the judge has ordered some form of punishment, penalty, or restraint on the alien's liberty to be imposed.

101(f)(3):

(f) For the purposes of this Act-No person shall be regarded as, or found to be, a person of good moral character who, during the period for which good moral character is required to be established, is or was--

(1) a habitual drunkard;  

(2) stricken by Sec. 2(c)(1) of Pub. L. 97-116.  

(3)     a member of one or more of the classes of persons, whether inadmissible or not, described in paragraphs (2)(D), (6)(E), and   18c/   (10)(A) of section   212(a)    of this Act; or subparagraphs (A) and (B) of section   212(a)(2)   and subparagraph (C) thereof of such section (except as such paragraph relates to a single offense of simple possession of 30 grams or less of marihuana); if the offense described therein, for which such person was convicted or of which he admits the commission, was committed during such period;