Yes - but they start accumulating wealth in their early 20s. That gives them at 10+ year head start on the average physician who finishes paying off their debts at ~35.
Software engineers aren't $200k+ in debt at 32 either.
If you are an average salaried software engineer, you can accumulate more wealth than a doctor if you invest at recommended rates. The break even point is somewhere around 60-65 years of age.
It's more difficult to gain admission to veterinarian school than medical school (in America).
Veterinarians pay about the same for their schooling (but they don't really have residencies) and vets make ~70k-80k/yr.
If we think of a job's salary as a function of the talents used by the job and the cost of admission to the job, it's unclear why doctors and vets should earn substantially different amounts of money.
But I agree that it's easier to accumulate wealth as a non-doctor than a doctor. Just treat the first couple years of your career like medical school and it shouldn't be too hard to crack 6 figures - if you live modestly outside a megaopolis, you can save 40k/yr and get a six figure headstart over a doctor.