Quote - Here is the tricky part.

What I see towards the end of that video is a scene with a time of 6:30pm.

Then when he applies gamma correction I see a 8:30am in the morning on a slightly foggy day.

If you use gamma correction to portray "daytime" your scene, FINE.

But instead of using gamma correction you could of just done the lighting correctly in the first place which will give better results since you're shooting for a realistic lighting position instead of a bandaid/quick fix aka Gamma correction.

That's my opinion. 

Instead of applying gamma correction to the end scene he should of just increased the lighting right?

You seem to be misunderstanding something vital.  Gamma correction isn't about good or bad lighting.  It's about not feeding the renderer gibberish (according to it) nor letting the renderer pass gibberish (according to the monitor) to the monitor.

Gamma correction is correction, not a band-aid.  Renderers understand and produce linear content.  They perform linear calculations, and pretty complex ones at that.  Digital images and monitors are in sRGB space, not linear space.  Colors don't mean the same thing to the renderer as they do to the monitor or the camera or software that produced the textures.  Linear workflow means translating sRGB textures into linear ones so the renderer can understand and handle them properly, and then translating the renderer's work to sRGB so the monitor can understand and handle it properly.  It's no more of a band-aid than, say, translating a Spanish text to an Italian, and then translating the Italian's response to Spanish for the author to read. 

All realistic renders incorporate some form of linear workflow.  You cannot do realistic shading in general without translation between linear and sRGB space yet use linear calculations and sRGB textures.  You can come up with cheats and workarounds that work for a specfic scene, but then you have to create a new compensation for incorrect results each time you make a new scene. 

Which isn't to say that no renderers use the more correct sRGB equations (Mitsuba does), nor that they don't have additional ways of adjusting your color space.  Poser itself has ways that bypass its GC option.  If you download Tate's free product rendering scene at RDNA, you'll find he does some really funky stuff with render settings that create a similar color space translation.  Blender has composite nodes to pass your render through before final output to screen (which is more useful than I can express).  Luxrender has all sorts of settings to mimic different types of physical film, which is awesome if you've ever experienced the difference film types can have on the richness and hue of skin tones or even polished wood.    But that issue of sRGB input, linear calculation, and sRGB output on the screen is always at the heart of producing realistic shading results.

Changing the lighting can only address part of the symptoms and won't touch the basic problem problem.  You can't actually correct the whole response with lighting, because sRGB content processed linearly and displayed in sRGB space produces a non-uniform effect.  It's not simply a matter of everything being brighter or darker or even more high contrast.  I can often spot those who don't use linear workflow by the yellow bloom, the way surface color and saturation overpowers ambient lighting effects, and the incorrect light fall-off, not just by the dark areas.  I myself had medium shades that looked as if grey had been dumped into that part of the image. 

You also lose information when you render with regular workflow.  There are steps between values and colors that are simply no longer there.  So even if you do lots of postwork, it can be easier if you start from a linear workflow basis because you have more to work with as a base.  Also, the way that regular workflow shades is fairly obvious and consistent across applications ane even machines.  So it can get in the way of producing work that has a specific and individual look, rather than a tool-based look.  It doesn't have to, but it can. 

That said, I've seen some great works that use regular workflow.  Many of my favorite artists use regular workflow, and produce stunning works with it.  Looking at my own work, I actually don't think it's a matter of one workflow producing better or worse results.  As Blackhearted said, it's more about having a vision and going with the easiest way achieving it.   The issue is more on the creation side.  If lighting is important to what you want out of your work (as opposed to, say, intricate objects and textures, narratives, etc.), then fighting the lack of translation in each image you make with materials and lights will generally mean a lot more work and probably more problems.  Just like it's generally quicker and more correct to turn on IDL and use some form of environment lighting (environment sphere, IBL, etc.) than try to imitate bounced light with lots and lots of spots, it's generally quicker and more correct to address the color space issue at its source with render settings.

I've gotten great shadows with linear workflow, even in the dark, just not so much with GC.   Gamma correction is an approximation that doesn't account for darks, whether through shading, color, cast shadow, etc.  For low light works, you have to fight the flattening of the exponential curve of gamma correction response.  It would have been way easier if Poser had implemented more accurate sRGB equations that have a linear portion for low values.  But they didn't, so I tend to use my less accurate but still (IMHO) a lot easier to work with materials with sRGB correction built in for very low light scenes.  They give me rich shadows just fine.   That said, material correction introduces errors with IDL.  So I find I have to balance the effort I need to take to correct the issues with using GC and losing a range of lower values, and the effort I need to correct the issues with using material-based correction. 

Oh!  And true HDRI are different because they're linear by nature.