I suspect that it takes any expression, then checks if the expression is valid.

Yeah, but even then, it will reject most expressions:

$perl -we 'my(f($x))'
Can't declare subroutine entry in "my" at -e line 1, at EOF
Execution of -e aborted due to compilation errors.
[download]

Now, my does return an lvalue, and ?: can, but that isn't enough in itself for it to be accepted by my:

$ perl -we 'my($x = 3)'
Can't declare scalar assignment in "my" at -e line 1, at EOF
Execution of -e aborted due to compilation errors.
[download]

What the reason is that my(my $x) and my(0?$x:$y) are accept isn't clear to me.

This one is interesting:

$ perl -we 'my(local $x)'
Can't localize lexical variable $x at -e line 1.
$ perl -we 'perl -we 'local(my $x)'
Can't localize lexical variable $x at -e line 1.
$
[download]

Regardless of the nesting of local and my, we get the same error message.

Mixing state and my:

$ perl -wE 'sub f {state (my $x); say ++$x} f; f;'
1
1
$ perl -wE 'sub f {my (state $x); say ++$x} f; f;'
1
2
$ perl -wE 'sub f {state my $x; say ++$x} f; f;'
No such class my at -e line 1, near "{state my"
Execution of -e aborted due to compilation errors.
[download]

Mixing our and local:

$ perl -wE 'sub f {our local $x; say ++$x} f; f;'
No such class local at -e line 1, near "{our local"
Execution of -e aborted due to compilation errors.
$ perl -wE 'sub f {our (local $x); say ++$x} f; f;'
1
1
$ perl -wE 'sub f {local our $x; say ++$x} f; f;'
1
1
$
[download]

So we can have our (local $x), local our $x, but our local $x doesn't parse.