Ok, first GH secretion is quite a complex process that is both directly and indirectly stimulated. It's not even close to as simple as stated above or even in my explanation.

But it atleast mine will be much closer to being accurate!
Regarding exercise, GH secretion is sensitive to these main stimuli:
1.Volume of exercise
2. The amount of rest between sets
3. Resistance used
4. Catecholamines, primarily epinephrine can also stimulate GH release.
Some of these stimuli or variables do lead to increased H+ and lactate concentrations, which in tern do increase GH release.
The last part, where it says, resulting in significant loss of body fat is not supported by any research I have ever seen. And I find it highly doubtful.
Moving along..
Most people, really have no clue how beta-alanine works or have a proper understanding of glycolysis, which is why there is so much weird information out there on beta-alanine.
The ANSWER is it affects BOTH!! It reduces lactic acid formation and fights the drop in pH caused by increased H+ concentrations. NOW

I have never seen anyone ANYWHERE explain how BA can reduce lactic acid formation and I wont actually be disclosing this either. But, I will say this, if you dig DEEP enough inside the pathways of glycolysis and TRULY understand how it works and how carnosine comes into play, you can understand how beta-alanine can reduce lactic acid formation. You will also understand, why lactate levels may stay the same or actually decrease, even when performance is increasing when supplementing with BA.

Yet another reason why measuring lactate in beta-alanine performance testing is not very helpful. VT tests are MUCH better.
I got into this exact discussion with some of the top phD researchers in the world and initially we came to one conclusion. In a nutshell, that lactate levels should actually increase due to glycolysis being able to carry on longer due to increased CARN concentrations soaking up more H+. But after some deep research myself, I came to a much bigger picture and I believe many of them agree with me now.
Based on how I believe beta-alanine can both reduce lactic acid formation but also allow increased lactate ion levels to occur, I would say NO significant affect one way or the other. Just in case you don't want to take my word, there is a beta-alanine study that actually showed that beta-alanine DID NOT alter GH concentrations.
Lastly, I don't think GH release during exercise matters that much to begin with, so it's kind of a moot point.

Most of GH's affects come through boosting IGF1 and guess what? IGF1 has been shown to increase during exercise INDEPENDENTLY of GH.