It's unfortunate that sources are not specified, but the methane emissions from rice paddies are well known, I believe. I didn't find absolute numbers, but OWID does list them as significant (though less than from animal): https://ourworldindata.org/emissions-by-sector#annual-ch4-em...

I did not hear about the rice-diabetes connection before, but "golden rice" was developed specifically to deal with the nutritional deficiencies caused by rice (over)consumption: https://en.wikipedia.org/wiki/Golden_rice