Expected result:
----------------
false

Actual result:
--------------
filemtime(): stat failed for {$path}

http://php.net/manual/en/language.types.string.php#language.types.string.casting

If you don't think the "Converting to string" section is relevant to your problem, read it again until it does.

it does exactly what the docs say, the only thing which should be fixed is the braindead warning for functions which return false in case of errors so that you don't need @ or a uselss file_exists() around the code

you likely miss one of the most important facts when working with PHP: ===, !== when compare values and when boolean false is converted to a string it's an empty string, since echo is working with string it does implicit typecasting and false is something completly different then the string 'false'

php > echo false;
php >

php > if(filemtime('nonexists') === false){echo 'NON-EXISTS';}
Warning: filemtime(): stat failed for nonexists in php shell code on line 1
NON-EXISTS