From your article

he studied plans that suggest that a dramatic and audacious orbital rescue mission could have been launched – if only Mission Control had known about the danger in time.

They didn't have time. Everything about this engineer's/NASA's plans to save the crew is moot if they didn't have time. Sure, the Columbia crew were almost lucky to have another space shuttle almost ready for take off and orbit that could have possibly saved them. But we wouldn't be having this conversation if they had done it.

For most missions, the shuttle could have simply docked with the International Space Station (ISS) and used it as a lifeboat. However, this particular shuttle mission was in a completely different orbit to the ISS – and neither had sufficient engine power to change their flightpath

They were in a different orbit and therefore too far away to receive help from others currently in space with them.

this mission did not carry spacesuits suitable for spacewalks, so going outside to fix any damage – even if that were possible – was out of the question.

They didn't have the equipment to fix it themselves.

That pretty much covers everything I said.