Since you already have an attorney, he should be able to advise you on that. What he probably told you is that in your specific case you qualify for the exceptions and therefore your petty theft conviction does not affect your immigration status.
But this can not generally be said for all cases. I am not quite sure what your current immigration status is, but this is the law:
Any kind of theft is a crime of moral turpitude.
If you are not yet in a permanent status you might be "inadmissible" if concicted for a crime of moral turpitude if this is the second conviction or if the conviction is for a crime that carries a maximum sentence of one year or more and you have been convicted to more than 6 months in jail.
If already are in status you are deportable (or removable as they say nowadays) if you have been convicted of a crime of moral turpitude within 5 years of admission and convicted for a crime with a possible sentence of more than 1 year in jail.
Petty theft mostly carries less than a year as a penalty, so in most cases one conviction does not affect immigration, but in some states petty theft can carry more than one year, so it depends on the state and the circumstances of the case. Also, if it is not the only conviction, often even jiust a petty theft conviction can lead to removability.