I disagree with your first sentence. Just because the end result is similar in regards to the career does not mean the training is identical, which is the original discussion in the thread. NPs and PAs have similar roles and responsibilities in the clinic, but a PA would never say they were in NP school or vice versa. Somebody with a masters in social work and a masters in clinical counseling can both go on to become counselors, but those degrees are not interchangeable.
For your second sentence, that's not "a similar argument" because I'm not making an argument about one curriculum being weaker than another. They are just different. Can a dental student say they are in medical school? What's the difference? They do 4 years of undergrad, 4 years of professional school, can do residencies, independently treat patients, prescribe medications, admit patients to the hospital, and perform surgeries too.
All US DO and MD schools have to meet certain criteria through the LCME and whatever the DO accrediting body is. Podiatry schools have different criteria. All US MD and DO schools offer the opportunity to take the same board exams. Podiatry schools do not. All MD and DO students have the opportunity to go into any specialty. Podiatry students do not.
And again: I'm absolutely not saying podiatry is inferior to other medical specialties. It's not. And if you are continually taking "different" to mean "bad," then perhaps that is a result of your own internal biases.