I read about a case once of someone tricked into answering a work e-mail, for their employer located in their home country while in the US for vacation, and for that they denied entry to this person. Honestly I'm not sure what I'd say in this case.
It seems that points of entry used by the typical traveler that enters through them, are better as they are more familiar with the local situation. If you are the odd one there, you might get singled out as they try to make sense of your story. So I'd prefer entering through an international airport close to where I'm going, than say, by car from Mexico. For now, I'd avoid entering through the south by car, but I don't think the same applies up north.
For your case specifically, threeseed already shared good guidance. Make your trip make sense to outer observants, don't offer them unnecessary avenues of questioning, and keep documentation and contact numbers at hand.