The behaviour you see is present not only in record structs, but also non-record structs too. Try removing the keyword record and the () after the name Record, and see the same behaviour.
This is just how calling mutating methods on structs are supposed to work. When you call a mutating method on a struct variable, say x.F(), you actually pass a reference to x, then that reference can be mutated by F.
For example, if Record is a non-record struct, and MyObject is not readonly, MyObject.SetDoSomething(true); is compiled to the following IL (Try it yourself with SharpLab):
ldsflda valuetype Record Program::MyObject
ldc.i4.1
call instance void Record::SetDoSomething(bool)
ldsflda means "load static field address". I've only found a small section of the spec that talks about this when it is talking about boxing of structs (emphasis mine):
Similarly, boxing never implicitly occurs when accessing a member on a constrained type parameter when the member is implemented within the value type. For example, suppose an interface ICounter contains a method Increment, which can be used to modify a value. If ICounter is used as a constraint, the implementation of the Increment method is called with a reference to the variable that Increment was called on, never a boxed copy.
Basically, if you don't box structs (you clearly don't here!), their methods are supposed to be called by reference. No copies are supposed to be made.
On the other hand, if you call x.F() but x is readonly, you obviously can't translate it to the same code above, since that would mutate the field. What the compiler does, according to SharpLab, is:
ldsfld valuetype Record Program::MyObject
stloc.0
ldloca.s 0
ldc.i4.1
call instance void Record::SetDoSomething(bool)
Basically, it loads the value of the struct to a temporary variable first, and then pass the reference of that variable to SetDoSomething.
var temp = MyObject;
temp.SetDoSomething();
Hence the "copy" behaviour that you see.