This is an interesting observation. But honestly I don’t think this is really hard to explain at all.

I think within the genre of comic books, your point makes sense. But if we’re applying a lens of realism (which I think CA:WS did well, and I wish more Marvel movies would), Tony’s network intrusion would not have been at all likely to have uncovered that SHIELD had been ideologically compromised.

What we see in Avengers is that Tony secured unauthorized access to read files to which he wasn’t afforded access. First, it’s not actually at all reasonable to assume that he had full access to all SHIELD data everywhere, ever. It’s split across thousands of servers and departments. It wouldn’t be universally accessible to anyone. This is true even for large institutions that aren’t highly, highly sensitive intelligence operations. But it’d be doubly so for one that is. Most likely, he would’ve grabbed unencrypted traffic that was local to the helicarrier, recently accessed, and titled or contained notable text that was relevant to their current situation. That could certainly yield shipping manifests or operational plans to use the tesseract for weaponry.

But – and this is really the key thing – even if he had the ability to access all SHIELD records, and had the ability to meaningfully digest this enormous trove of information, it would still be incredibly hard to see that SHIELD was compromised. There aren’t going to be any emails that say “Hey Bob: did you kill Mike for finding out that we’re both Hydra foot soldiers? Hail Hydra, Lisa”.

Infiltration is a process of persuasion and carefully installing dual loyalists in key positions to compromise decision making processes, as you describe. It consists of grooming intelligence assets and identifying who can be trained to groom additional assets. That all takes place primarily through interpersonal conversations. There’s very, very, very little documentation of it in a file system that would reveal it if you didn’t already know about some compromised asset. To the outside world, all of HYDRA’s goals look so much like those of a modern international peacekeeping body that the only secret they need to keep is who the guns are pointed at and who has their fingers on the triggers. Which is fundamentally a key point of the movie.