Let's start with defining some terms, so that we're all talking about the same thing.
The primary operators are postfix "x++" and "x--", the member access operator "x.y", the call operator "f(x)", the array dereference operator "a[x]", and the new, typeof, default, checked, unchecked and delegate operators.
The unary operators are "+x", "-x", "~x", "!x", "++x", "--x" and the cast "(T)x".
The primary operators are by definition of higher precedence than the unary operators.
Your question is
is there a situation where x++ having same level of precedence as ++x would cause an expression to return a wrong result?
It is not at all clear to me what you mean logically by "the wrong result". If we changed the rules of precedence in such a way that the value of an expression changed then the new result would be the right result. The right result is whatever the rules say the right result is. That's how we define "the right result" -- the right result is what you get when you correctly apply the rules.
We try to set up the rules so that they are useful and make it easy to express the meaning you intend to express. Is that what you mean by "the wrong result" ? That is, are you asking if there is a situation where one's intuition about what the right answer is would be incorrect?
I submit to you that if that is the case, then this is not a helpful angle to pursue because almost no one's intuition about the "correct" operation of the increment operators actually matches the current specification, much less some hypothetical counterfactual specification. In almost every C# book I have edited, the author has in some subtle or gross way mis-stated the meaning of the increment operators.
These are side-effecting operations with unusual semantics, and they come out of a language - C - with deliberately vague operational semantics. We have tried hard in the definition of C# to make the increment and decrement operators sensible and strictly defined, but it is impossible to come up with something that makes intuitive sense to everyone, since everyone has a different experience with the operators in C and C++.
Perhaps it would be helpful to approach the problem from a different angle. Your question presupposes a counterfactual world in which postfix and prefix ++ are specified to have the same precedence, and then asks for a criticism of that design choice in that counterfactual world. But there are many different ways that could happen. We could make them have the same precedence by putting both into the "primary" category. Or we could make them have the same precedence by putting them both into the "unary" category. Or we could invent a new level of precedence between primary and unary. Or below unary. Or above primary. We could also change the associativity of the operators, not just their precedence.
Perhaps you could clarify the question as to which counterfactual world you'd like to have criticized. Given any of those counterfactuals, I can give you a criticism of how that choice would lead to code that was unnecessarily verbose or confusing, but without a clear concept of the counterfactual design you're asking for criticism on, I worry that I'd spend a lot of time criticising something other than what you actually have in mind.
Make a specific proposed design change, and we'll see what its consequences are.