I struggled with constant invalid URL errors for a calendar I wanted to use. The file validated, the URL was correct.
Finally, it turned out that I was running PHP 5.2.13. This version has a bug in filter_var(..., FILTER_VALIDATE_URL) that reported URLs that had a hyphen (-) in the host name as invalid. Sure my URL used the ical-mac.com service, which had a hyphen.
I'm on shared hosting and cannot update the PHP version easily, so for a interim fix I changed amr-import-ical.php#87 to
$u = $url;
Don't know how much of a security risk this is, but now again, the plugin works even on PHP 5.2.13 with webcal-URLs that have a hyphen in their host name.
HTH for anyone having the same issue,