Just because a B&S engine has an oil filter doesn't mean that it isn't still a "splash" lubricated engine. MOST B&S engines are splash lubricated because it is an effective, efficient, reliable, light weight, and inexpensive oiling system. Splash lubrication systems have been in wide-spread use since the dawn of the internal combustion engine.
When B&S first introduced filters on their OHV engines there was of course an oil pump also. This oil pump simply picked up the oil from the sump, ran it thru the filter and dumped the oil back out into the sump. Shortly, they started routing the discharged oil to the bottom main only, where it returned to the sump, that way they could say it was "pressurized". Note two things here, the bottom main bearing has never been a problem on B&S engines (because it is fully immersed in oil) AND IF the B&S engine is truly pressurized, it will say "fully pressurized", not just "pressurized".
Interestingly, Tecumseh vertical crankshaft engines have ALWAYS had a simple oil pump that pumped the oil through the cam shaft up to the upper crankshaft bearing where it discharged down onto the connecting rod bearing and cylinder to lubricate them "splash" style.
