There is not much of API, but an ordinary GET HTTP Request behind this function. I just tried this simple code
http://www.news2news.com/vfp/?example=175&function=268

at the same time capturing the TCP exchange between my computer and the server (I use EtherDetect software).

This is the request, my computer sent to server when I initiated the URLDownloadToFile call:

GET /vfp/downloads/w32data.zip HTTP/1.1
Accept: */*
Accept-Encoding: gzip, deflate
User-Agent: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1; .NET CLR 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50215)
Host: www.news2news.com
Connection: Keep-Alive

The server responded with the headers

HTTP/1.1 200 OK
Date: Wed, 21 Dec 2005 20:28:08 GMT
Server: Apache/1.3.33 (Unix) mod_ssl/2.8.22 OpenSSL/0.9.7e
Last-Modified: Sat, 23 Feb 2002 22:16:12 GMT
ETag: "4dab6b-6ca9-3c7814ac"
Accept-Ranges: bytes
Content-Length: 27817
Connection: close
Content-Type: application/zip

and immediately after that transferred the requested file.

Try to use any packet sniffing software to check what is your server sends back. Also what is the value the URLDownloadToFile returns in your case.

Also note that this function may retrieve a cached file when its timestamp is the same as the remote file has.