No. Some pets do have dietary restrictions. This dietary restriction can be permanent or momentary, but they do exist.
My youngest (in age, and also the last in being adopted) cat, who had lived three years on the streets until she appeared at our doorstep, came not having eating well (or at all) for who knows how much time (she was malnourished) to the point that she couldn't tolerate the food my oldest cats ate, so she was prescribed special food for her, so she'd have an easy time adjusting herself to eat everyday ones again (or for the first time, as we don't know if she ever had a home before, or if she was born in the streets). Now, three years later, she's doing great and fully eating common cat food (which she began to do last year).
But, vets always have brands that they advertise for. The brand ours advertise is too expensive, so we went/go another route for both the common food and the dietary restriction food. Luckily a friend of my mum has a pet shop so she could get us the cheaper, but equal in content and quality, food brand for us.