Until recently, my interpretation of "I would argue that (..statement..)" was "My opinion is (..statement..) and I am willing to justify it", in other words - author put stress on subjective matter of the statement that coud be put into dispute. I think that this is used when there are people that disagree, because opinion is controversial, and/or not commonly accepted. "Arguably" seems to have similar usage; phrase "According to meteorogical data this was the greatest rain of the century." is stating a fact, an scientific thesis, but "It was arguably the greatest rain of the century." means (for me at least) that author share his opinion, but he is aware, that someone else might deny.
The problem is, that "to argue" has basically two opposite meanings:
- (1) To show grounds for concluding (that); to indicate, imply.
- (2) To debate, disagree or discuss opposing or differing viewpoints.
The consequence is that all phrases inherits uncertainity about interpretation, unless they are idiomatic. Beside this, even when second meaning is used, there is still the question - if author defend the statement, or stand against it? After all that analysis, I am no longer convinced whether: "I would argue that it was the greatest rain of the century" roughly means "I think that (..)" or "I am not sure if (..)". After some search I found only this blog entry, but it havn't resolved my doubts. This language construction seems to be prone to context of use.