This is actually a myth. At the end of the day, you've burned off just as many calories as you would have if you worked out later in the day. The results, are going to be the same with only very minimal differences. Definitely not enough to make up the difference, nor enough to make someone say "ah, a 5am run wil be a lot better than a 5pm run".
I've heard people try and say "But your stomach is empty, so you're burning calories you already haven't eaten yet so you force your body to use its own fat for energy!" but that's also, a little bit false. Yes, it's true in theory that because you have eaten nothing yet, you are forcing your body to go into "Starvation mode", in which it actually STORES fat in order to sustain you. This is why diets where people literally starve themselves rarely work. Not to mention that you are working out WHILE your body is in starvation mode.. And anyone that's worked out knows what happens when you work out.. You get tired, you spend energy, etc. This is going to do nothing but FORCE your body to go further into starvation mode (I actually have a calculator that goes through what percentage of body fat you likely have, versus all kinds of factors, and then determines what percentage of starvation mode you'll be in for the calories you're eating). This can be both extremely dangerous, especially if weight lifting, and also prolong your hope for getting noticeable results.
So.. In essence, yes what you said is correct, but misleading to a degree. There are many differences of opinion and no solid studies have ever been done to my knowledge that difiinitively proove that working out in the morning will yeild better results. It could also be a person to person basis, as throughout my training career I've exercised many different routines. I gained (muscle) and lost (fat) at the exact same rate I was prior to working out in the mornings. I no longer work out in the mornings.
As far as I have been taught, most of the benefits that come from working out in the mornings are mental, like feeling more alert and being able to start your day earlier now that you've developed a routine. Not to mention that you've gotten your workout out of the way for the rest of the day so you're more likely to actually do it.
But personally, if I had a client come in and ask me if they did a cardio session aiming to burn 500 calories off which time would be better to do it, 5am or 5pm... I'd kindly remind them that 500 calories burned at 5am, is exactly the same as 500 calories burned at 5pm. The glycogen factors in for these people very little. Weight trainers will rely on it a lot more if they work out in the mornings but not people that want to burn fat. Again, the starvation mode your body goes into from not eating will completely negate the fact that you've got a little boost of glycogen in your body from not eating.
Never, EVER, should you work out on an empty stomach. Cardio or weight training. It will do you absolutely zero good. It can even lead to a lot of disorders, such as GERD and increased acid reflux due to lack of stomach contents.
It is true however, that you should never work out at least 2 hours prior to bed time. You usually will have so much energy and have difficulty falling asleep. Luckily, I am not one of these people, but if my girlfriend works out for even 20 minutes within a few hours of going to bed, she tosses and turns almost all night.
It sucks doesn't it? I refuse to wear a CPAP. There is no chance of that happening. I've got Apnea as a side effect from severe GERD and LES, but it's not your usual apnea. I've read and heard from my doctors, that your usual apnea episode lasts about 10-30 seconds, whereas mine are extremely quick, probably less than a second in length. Nevertheless, it's extremely annoying.
On topic though... I've found that a nice hard cardio/weight training combo really puts me to sleep if I give myself at least a 4 hour window from when I plan on going to bed. I pass out like a baby.
EDIT: Yes I know I need to edit the workout part but it's too early in the AM right now and I could care less to be completely specific about it