It was quite easy to get high tensile strength steel in 1916 - carbon is what you oxidize from bloom iron to make steel, it also makes steel strong - ductility and toughness is the goal in purifying and alloying steel.
Burning the carbon and other impurities down to make the steel as ductile as possible and prevent brittle fracture in industrial applications was generally the goal of steelmaking. You make pipe and tubing to contain pressure. You buy it off the shelf and use it.
Low carbon steel had all the strength they needed. (But they used medium and high carbon steels as well in high strength applications - structural flanges, nuts and bolts, bearings) - when you're containing pressure, ductility is more important than strength.
They certainly had seam-welded pipe in 1916 - that was all they had, they didn't pierce billets to make seamless pipe, and it would have been gas pipe and that's also what they made all bikes from. Bessemer-process steel was industrialized in 1856 and continually improved since.
You find old bikes, especially prewar bikes, it's easy to feel the seams in the tubing, and that's why they call them gas pipes. You may find seamed tubing used in a Flying Pigeon or early postwar Japanese bike.
TI built their company around piercing billets to make seamless tubing. High strength alloy steel tubes are generally for lightweight structural applications and back then for airplane frames. Since these also made better bikes, it was a natural growth for TI to move into making specialty tubes for bicycles and eventually the whole bicycles. (The history is essentially the same is for Reynolds, Columbus, Vitus, Tange, True Temper).
But certainly most of the bikes being discussed here are newer than that date, and generally are bike boom bikes or even newer than bike boom, and they're all seamless tubing. Price a Mead, Dayton or Flying Merkel - they're not what's usually being discussed here.
