Convert HLS MP4 to standard without re-encoding?

[hidef_rec]

I'm using Simple.tv, which records OTA TV as MPEG4, but in 3 different HLS streams. They classify these as "Good", "Better" and "Best". I only choose "Best", which is a 1080p MPEG4 HLS file with AAC audio. I can play this on my PC with VLC, MPC-HC, etc., but not in media players, XBMC, etc.

Is there a way to losslessly convert a HLS MP4 file to standard MP4?

Here's MediaInfo for a sample HLS video...
General
ID : 745 (0x2E9)
Complete name : C:\Users\HTPC\Downloads\Seinfeld - s3e17 - The Boyfriend.mp4
Format : MPEG-TS
File size : 1.09 GiB
Duration : 31mn 59s
Overall bit rate mode : Variable
Overall bit rate : 4 881 Kbps

Video
ID : 49 (0x31)
Menu ID : 1 (0x1)
Format : AVC
Format/Info : Advanced Video Codec
Format profile : High@L4.0
Format settings, CABAC : Yes
Format settings, ReFrames : 2 frames
Codec ID : 27
Duration : 31mn 59s
Width : 1 920 pixels
Height : 1 080 pixels
Display aspect ratio : 16:9
Frame rate : 29.970 fps
Color space : YUV
Chroma subsampling : 4:2:0
Bit depth : 8 bits
Scan type : Progressive

Audio
ID : 52 (0x34)
Menu ID : 1 (0x1)
Format : AAC
Format/Info : Advanced Audio Codec
Format version : Version 2
Format profile : LC
Muxing mode : ADTS
Codec ID : 15
Duration : 31mn 58s
Bit rate mode : Variable
Channel(s) : 2 channels
Channel positions : Front: L R
Sampling rate : 48.0 KHz
Compression mode : Lossy
Delay relative to video : -32ms

[Guest]

C:\Users\HTPC\Downloads\Seinfeld - s3e17 - The Boyfriend.mp4 Closed for rule 6 violation.