The problem is that hypothetically any tools you use on a computer could be compromised (by their compiler, or otherwise) to not show you truthful results on your screen. IDA Pro (and other tools at your disposal) may recognize certain patterns in binaries and know to show you a transformation of those patterns instead. This transformation would essentially be the reverse of the transformation that the compiler performs.

If you are able to inspect the actual contents of the program, not the output of a program that itself inspects the actual contents of the program, then this problem disappears. You have to examine the machine code without an intermediary program that could lie to you.

(Of course it is very unlikely that IDA Pro, objdump, or even 'od' is compromised in this way, but I would say this class of attack is largely hypothetical and implausible already...)

Edit:

From wikipedia: "What's worse, in Thompson's proof of concept implementation, the subverted compiler also subverted the analysis program (the disassembler), so that anyone who examined the binaries in the usual way would not actually see the real code that was running, but something else instead."