FLV Recorder captures packets from the flash player so IMHO it can capture more streams form member sites. Its recording abilities shouldn't be affected by timestamps, cookies or user-agent checking.

HTTP flash video streams are usually cached. And Replay AV can get them from the cache unless you use some web browser like Opera. But you can always open a cache folder manually.

RTMP Flash video streams can only be recorded by the above mentioned FLV Recorder as well as Replay Media Catcher and Orbit Downloader. But if I'm not mistaken they can be protected by timestamps only.

Are you sure the web-site uses flash streams? Can you PM me the stream URL? Please also post the web-site URL so that I can try to find some information about their broadcasts.