Why can't root execute when executable bits are not set?

In short, because the execute bit is considered special; if it's not set at all, then the file is considered to be not an executable and thus can't be executed.

However, if even ONE of the execute bits is set, root can and will execute it.

Observe:

caleburn: ~/ >cat hello.sh
#!/bin/sh

echo "Hello!"

caleburn: ~/ >chmod 000 hello.sh
caleburn: ~/ >./hello.sh
-bash: ./hello.sh: Permission denied
caleburn: ~/ >sudo ./hello.sh 
sudo: ./hello.sh: command not found

caleburn: ~/ >chmod 100 hello.sh
caleburn: ~/ >./hello.sh
/bin/sh: ./hello.sh: Permission denied
caleburn: ~/ >sudo ./hello.sh 
Hello!