Nonetheless, a couple aspects of the post by eileenf are important.
Among these is the issue of a Canadian resident driving a U.S. registered vehicle into Canada. Sooner or later this will become problematic. While enforcement seems lax, eventually there is a substantial risk the vehicle will be seized. And it will likely become, even before that, something that triggers further scrutiny.
Another is that an individual can only be "resident" of one jurisdiction at a time, and this is true despite the extent to which people in fact use multiple residential addresses relative to different purposes. There is no question about it being OK. It is not. There is some question about to what extent a person can get away with it, which is in many, many contexts, a lot, a real lot. But when it comes to those things relevant to and connected with crossing the border, doing this tends to become a lot more problematic . . . at least eventually.
And, as of this summer Canada is supposed to be keeping track of Canadian citizens cross-border movements, going both ways (exit info as obtained by U.S. entry records), and this is specifically in part for the purpose of better monitoring of benefit entitlements. Whether the program underlying the J-1 U.S. visa is in the scope of this I do not know. But no advanced degrees are necessary to discern what is at risk if the U.S. or Canada discover a person is using different residential addresses in order to remain eligible for the program . . . fraud is not ordinarily a good rung to climb in one's career ladder.
Overall, border crossing (even with Nexus) is increasingly a point of intense monitoring, if not overtly deeply intrusive scrutiny. I have not looked at Bill C-51 in depth, but I believe that some of the regulatory changes recently being proposed in relation to IRPA and the Citizenship Act, regarding inter-agency information sharing, are also related to some of the information sharing provisions in Bill C-51, in the sense that if and when Bill C-51 becomes law, the scope of the information sharing regulatory changes already in process will dramatically expand.
You used the word "conflict," relative to which I would caution that you are probably talking about contradictory information, and if you are the person who is the source of the contradictory information, it bears keeping in mind that since both cannot be true, if they are contradictory, one is ipso facto false, and providing false information in any connection with border crossing is, well, a recipe for things going off the rails, way off the rails.