Spacecraft-to-spacecraft transfer does not require a 'tunnel', just a static line and enough spacesuits for the people you're transferring. Everybody has a spacesuit because they wear them during launch - and for a short time a simple bubble would suffice!
String a wire between the two airlocks using the existing safety line clips, and 'zip' along. Perhaps five minutes each, plus airlock cycle and suiting-up time. Last guy out is a bit more fiddly as you can't put NASA spacesuits on without help, but not insurmountable.
This does need an MMU to get the static line set up (and maybe dismantled), so send that in the rescue craft.
As they hadn't planned a spacewalk in the mission, presumably there weren't any MMUs on Columbia and thus the only way to look is sat on the end of the arm. Don't think that reaches underneath so would have to send a person rather than simple camera.
While that isn't the kind of thing you just "pop out" to do, they could have done it had NASA accepted the need to take a look.
I suspect the real reason they didn't look was indeed "What if we find something?"
A very human fright response, and the same reason lots of people don't go get tested for cancers when they first suspect, instead waiting until it's too late to do anything.