What I gather from the OP is that their wife seems to live with them, as in share a residence. Otherwise, why would they both share a lease like OP says? It seems she’s constantly going to different places because of her research job, yet she maintains residence with her spouse at their home (this doesn’t mean, however, that they have to be together). If this is the case, that the wife keeps residence at the same address as her spouse (i.e., she uses it legally for her bank documents, taxes, voter registration, etc.), then OP doesn’t have to claim “ignorance.” She legally resides at their joint address, especially if she often travels back to be with her spouse for periods of time. This has even more weight if they file taxes together using OP’s address. She voluntarily took a job that requires her to relocate, like somebody else pointed out. It’s not the same as she voluntarily relocating for some other reason.
Like yet another person pointed out, the most sensible approach here is not to volunteer any information. So, ask your wife to come with you, bring pictures of you two (also keep some Skype screenshots at hand in case her living away comes up), and restrict yourselves to honestly answer only what is asked. If your wife usually lists your joint address on everything she does, it is proof that she considers the place you two rent her home. Make sure that she bring paperwork that shows her relocation is necessary for her job (for instance, some employer document that states that she would need to go to place X if she wants to do research on something). You mentioned your wife is a researcher, so you may qualify for an exemption anyway (should the subject come up) if she works for one of the institutions listed here.