Re, how you begin such an investigation, I think you've said it...
What you start with is a review of the carrier's procedures and the lee way allowed the captain. It's pretty difficult for the FAA to do anything after the fact, other than review procedures.
And perhaps connect the dots with facts such as the METARS.
By "investigation" is not meant the wholesale pursuit of a violation but a questioning and establishing of what occurred with the IB flight at BOS. From the initial post, something happened of sufficient import to warrant comment by both ATC and other crews. What was it?
If departing with contaminated wings is against the FARs (as it is against the CARs in Canada), and it is reported that that occurred, then establishing the facts as best as possible is required if only to review said procedures.
The "Ice Police" in Toronto sat at the end of the departing runway a number of times in my recollection. Their presence was highly controversial for the same reasons that the present matter is and the few times they charged a crew with a violation certainly heightened the controversy and the resulting fight to exonerate the crew was a strong one indeed. As far as I am aware, such "interventions" occurred after de-icing
which simply added to the controversy of "who is in command". I believe the process is no longer used but perhaps someone now operating out of Pearson can verify this.
Our own de-ice procedures provided for co-authority of the Lead or the Captain and a decision by one to de-ice could not be over-ridden by the other.
Invariably, with precip, esp possibly-wet snow (could it make a snowball?), and at the temperatures indicated in the METARS as provided above, de-icing was as automatic as it could be while still permitting some leeway to judge circumstances. In the early days, (when formal de-ice procedures were being implemented and equipment designed), if the temp was much colder, (ie, -25), some consideration was given to the fact that, if the metal was clean underneath, (as inspected, usually by gloved hand) but the wings were covered with a "light dusting", no de-ice was called for because there was no adherence of the contaminating material, (and it couldn't make a snowball). Often, ropes and brooms would be used to clear off such contamination. Today, no such freedom exists to taxi out and take off even with this kind of contamination.
Whether such awarenesses and procedures exist at IB could be one series of questions. The assumption here is not to question the commander's authority but to examine by what procedures the captain had at his/her disposal for guidance. I know it is trite to say that a commander's authority cannot alter wing contamination but I should think this is more about procedures than about such authority. I think it is entirely reasonable to examine any company's procedures which permits an aircraft to depart with contaminated wings. So far as establishing facts, that would be done the usual way.