Not true about "blood grooves" (proper term = fuller) about them stiffening or strengthening a blade. What it DOES do is lighten the piece without SIGNIFICANT weakening of the piece. Think of an I-beam construction. Is a 4"x4" cross-section I-beam as strong as a solid bar of steel of the same dimensions? Hell no. But it's still quite strong and a whole lot lighter.
What it does impact negatively is lateral strength. For example, katana with bo-hi are more prone towards bending or taking a set if they are used with improper technique (rolling through the cut, improper edge-alignment etc.) To use the I-beam analogy again, try bending an I-beam as compared to an equally-dimensioned bar. A whole world of difference.
Where the confusion comes in is when people confuse removing material to make the fuller with building up material around a thinner blade to make it stronger. There were rondel daggers that have been found with T-shaped cross-sections. As they were intended for use in the gaps of armor or to separate the links of maille, adding the "back plate" to give it a T shape stiffened the blade, as this was added material, not removed.
Hope that clears things up.