I think part of that is because they are too lazy to update the manual. Also Briggs says THEIR synthetic multi weight is OK.
Newer technology multi weight oils don't have viscosity break down like older multi weights did.

Kohler specifies 10W-30 instead of a straight weight oil.

You can down laod an ENGINE owners manual from the manf. website. I'd defer to that over the tractor manf. recommendations.

Oil viscosity is a nominal number anyway. They run a batch. If the viscosity ranges between 26 & 34, it's packaged as a 30 weight, since they don't have 25 or 35 weight oils.
One batch of 30 weight may be a noticeably different viscosity from a different batch and still be labeled as the same viscosity.