While I continue to disagree that Bryan Krause is necessarily correct and would need much more information on the actual funding chain to make a determination, I will offer the following advice.
Whether or not it is a real conflict of interest, your career would probably be better served by assuming that it is, rather than the opposite. This is, perhaps, an overly conservative approach, but it is safer for you to state it as a possible conflict than to deny that it is unless you can determine otherwise.
Thus, in my view, the theoretical and philosophical view may be in conflict with the practical view, you would be best served by taking a cautious stance. You are the one that is at risk here, not the commentators, so you should protect your reputation as best you can.
Your PI, of course, may have something to say about this issue.
A conflict of interest arises when you receive something of value as an inducement to provide a particular answer in your research, whether that particular answer is specified or not.
One can have an issue, even when doing proper research as exemplified by the following. Suppose a company (say, big tobacco) provides funding for 100 separate statistical studies. In the nature of things, some of those will produce results different from those of the population as a whole, say five of the 100. If you aren't allowed to publish separately, the company can then advertise only those studies which match its desired outcome, even though all 100 researchers carried out their studies completely honestly. In fact, this sort of thing seems to have happened in the past, hence the caution required of honest researchers. You don't even have to "bend to the will" of the funders to have a bad outcome here. Statistics itself leads to such a result unless all of the studies can be published.