It most certainly was a proof:
Assumption: B lies.
Fact: B claims H has nukes
Conclusion: B's claim is not true

Uh, no. This only follows logically if B lies all the time. In 2003 that was looking likely, but not certain, and certainly not proof of anything.

It turned out in retrospect that he lied maybe 95% of the time. But that fact wasn't available in 2003.

A rational person can still disagree with you by disagreeing with some of your unstated underlying assumptions, such as e.g. that H had actually had them built fully rather than only partially say, or that he had them smuggled in, or that a workable program is much less expensive than you believe etc.

But there was no absolutely evidence to support any of those claims.

You're sounding like the people who said that Saddam really did have WMDs but... they were smuggled to Syria, which is why they were never found.

There's a vast uncrossable gulf between that kind of narrative logic, in which anything goes as long as it sounds vaguely plausible, and evidence-based argument, which requires a decent data set to argue implications from.

Unless you happen to be a WMD scientist, all of your assumptions about H and his country were derived from interpreting media reports available to you, together with the meta-assumption that these reports were not all outright lies and misinformation.

That and reading books and comments by the UN weapons inspectors, who might reasonably be expected to have a more accurate picture than the media.

In fact the media were spectacularly wrong and generally supportive of the party line, so there was no meta-assumption needed.

I assumed the primary sources - which were freely available to anyone - were more accurate than the media reporting.