Yes, it is very likely that he truly has HSV 2. People who have HSV 1 first and then acquire HSV 2 often have very limited or no symptoms with HSV 2 acquisition. Your risk of becoming infected by him is lower for two reasons: 1) he’s been infected for a long time and 2) he is asymptomatic for genital infection.
The IgG results for HSV 1 are always a lot higher than they are for people who have HSV 2. I’m not sure why that is, but it is.
If he used condoms and took daily antiviral meds, your risk of acquiring HSV 2 from him would be very low.