This advice for drinking vinegar for acid reflux/GERD is not something I've been able to find any credible backing for.
The OP's source for the claim being draxe.com suggests they are talking about this page which, as the OP has correctly determined, is full of contradictory and confusing advice.
Along what appears to be a pretty poor grasp of how digestion, biology and chemistry works.
This perhaps unsurprising given that "Dr" Josh Axe is not really a doctor in the medical sense at all, but rather a nutritional supplement and essential-oil salesman and chiropractor.
And it's the first characteristic here that's important - "Dr" Axe's page isn't giving medical advice it's selling supplements, and this is why the apparent contradictions come about.
First the page more-or-less accurately points out that acid-reflux is caused by stomach acid making it's way into the esophagus and that the basic first-line approach to treating acid-reflux symptoms is to use either over-the-counter antacids (to neutralize existing excess acid), and in more chronic cases H2 blockers and/or proton pump inhibitors (PPI) to reduce the acid production.
The claim is then that these don't provide lasting relief since any attempt to reduce the stomach acidity can only be temporary since the body will naturally produce more to restore normal pH levels in the stomach, while this is true in the case of antacids H2 blockers and PPI drugs don't work by neutralizing acid but by inhibiting it's production in the first place.
And the further claim that they only treat the symptoms not the causes is actually not enough stomach acid:
Hypochlorhydria, the clinical term for low stomach acid, is an under-researched and dangerous condition. Every time you take antacids, H2 blockers or PPIs, you are contributing more to this problem (which may be one reason you develop heartburn in the first place). Prolonged hypochlorhydria leads to chronic atrophic gastritis and is associated with side effects including vitamin B-12 deficiency, autoimmune conditions, asthma, diabetes, chronic fatigue and many other disorders. (24)
Yes, you read that right - the supposed reason why people experience acid-reflux is because they don't have enough acid. As I said earlier I can't find a single solid scientific source to back this up - whereas there are studies to that the conventional view is accurate.
Now hypochlorhydria/achlorhydria is a real thing, where gastric hydrochloric acid levels drop below the levels required to properly digest and absorb food and it's possible to experience some indigestion-like symptoms but I can't find any solid evidence to back up the notion that this causes acid-reflux/GERD. And it feels fairly counter intuitive to boot.
Over (either through long-term use or excessive dosage) or inappropriate use of antacids or PPI drugs can potentially result in hypochlorhydria but the treatment for that scenario is to discontinue PPI treatment. This isn't the only cause of it but it's perhaps the most common and easily treated since the body will resume normal gastric acid production once the treatment that suppresses it has been stopped.
So I'm supremely unconvinced by the hypothesis that the majority cause of acid-reflux/GERD is a lack of stomach acid. But let's stick with it for a moment because this is the basis for the "drinking vinegar claim", specifically:
Although no official studies have been conducted on the impact of apple cider vinegar on acid reflex and GERD, anecdotal evidence seems to support that it can be an incredible natural remedy for acid reflux.
and leads to the following recommendation:
Raw apple cider vinegar is also a must-have for anyone trying to boost stomach acid levels. Because vinegar is naturally acidic, it will natuarally lower the pH in your stomach. Additionally, AVC helps control candida overgrowth, a known cause of low stomach acid. I recommend taking 2 tablespoons of apple cider vinegar in one glass of water 3x daily to help cure low stomach acid.
The notion that you would "treat" that by drinking diluted vinegar as some kind of substitute or supplement for gastric acid (which is about ph 0.8 when secreted and is diluted to between pH 1 - 3 in the stomach) is at best moderately absurd.
Even the most acidic vinegars are essentially an already diluted form of acetic acid (a mild acid with a pH of ~ 2.4) and apple cider vinegar is ~ pH 5. (It's important to remember when comparing pH values that the [pH scale] is logarithmic, so stomach acid with a pH of 1.5 is actually ten times more acidic than vinegar with a pH of 2.5.
Those pH numbers are only going to be rising (i.e. getting less acidic) when you dilute them as the "Dr" Axe site suggests.
During the gastric phase of digestion (i.e. when you're putting food into your stomach) the distension of the stomach and presence of the amino acids from the food triggers the secretion of large amounts of gastric acid lowering the pH in the stomach to just above 2 so unless you are already completely achlorhydric it's actually going to decrease the acidity in the stomach (although not as much as say tap water at pH ~6.5-8.5) and if you're completely achlorhydric some acid-reflux symptoms are going to be the least of your worries.
So if anyone's ever reporting any benefit from drinking apple cider vinegar with regards to their acid-reflux/GERD symptoms it's not because it made their stomach more acidic!