If he can show that his last entry was with inspection by US government officials, he likely can successfully apply to adjust status in the US. The reason why the border inspector let him in in '00 may not be relevant as to his adjustment of status now. For whatever reason, he was let in. Back then, before 9/11, border inspectors were somewhat more lenient. If someone did not appear to be troublesome, the inspector likely would let him in.
What you and he likely should do is collect all the records and review them with an attorney again to see if any potential problems can be spotted.
I agree that your husband will likely be able to adjust his status and get his greencard since he last entered on a visa and is now married to a U.S. citizen. However, he may need a special waiver for two possible reasons. First it appears on his first stay he may have overstayed since he remained in the US for 13 months. Typically tourist visas allow entried of a maximum of 6 months. If he overstayed by more than 6 months, he could have incurred a bar of admissibility for 3 years. That bar can be waived with a waiver application. But you would need to discuss in more detail the dates of his entry, allowed stay, and departures in more detail with an experienced immigration attorney to determine for sure if he indeed incurred this bar. Also it is an issue that sometimes the immigration officers reviewing the case sometimes miss. Also you should review carefully with an attorney what statements were made when he reentered and was questioned by customs. If he made any false statements to the customs official, that could incur the need for another waiver. I would recommend that you and your husband go have a consultation with a reputable immigration attorney to review these issues in detail. Just by having a consultation does not obligate you to hire that attorney to complete the matter. But you can at least make an informed decision having discussed the risks and potential complications with an attorney.