Generally, it's hard to be an imposter in any field, interdisciplinary or not. (This includes English, despite what the following XKCD comic suggests.)
If a PhD program is interdisciplinary or encourages interdisciplinary work, then they will likely require PhD candidates to have at least one committee member who is an expert in each discipline. For example, a PhD candidate in English who focuses on connections between medieval art and literature might have two committee members in medieval English literature and a committee member in art history. Each committee member can verify that the parts of the dissertation dealing with their field and subfield and its methods (archival transcription, visual exegesis, close reading, etc.) work well. A good supervisor will ensure the candidate practices due diligence in matching their interests with their committee choices.
Is it technically possible that work will get through where neither the student nor the committee members understand the methodology of the project? Yes, if the supervisor isn't doing their job and the committee members, the student, the chair of the department, and the dean of the graduate school raise no flags. For even a minimal approval process, that is six people (a student, three committee members, a chair, a dean*) who all have to be incompetent or negligent about guiding a PhD candidate through the dissertation.
Less prepared candidates sometimes do get their degree, but usually the minimal expectation that you have someone from each subfield on your committee reduces the likelihood of that occurring. Furthermore, if somehow the department or the school didn't catch on that someone is graduating from a math program with (a) a bioinformatics specialty and (b) no biology or bioinformatics experts in the department or on the committee, the job market provides another degree of scrutiny, as committees look at not only candidates but also what their graduate programs are known for. (Where is your degree from? Is its reputation for interdisciplinary research well-known?) Journal editors provide even more scrutiny, as editors for credible journals are often familiar with the field(s) the publication will enter. None of these checks are foolproof, but they add friction at various stages of approval.
*In my experience, the dean officially approves of a dissertation, but pragmatically it's the person in the dean's office who actually reads the manuscript and checks it for formatting, signatures, and other elements. So, that person.
