Step 1: Fail at reading comprehension.
Step 2: Complain about a misunderstanding.

Yup, FFXIV forums.

@AuctionGirl: you've got it way wrong. Let me try to clear this up for you in the simplest terms.

Quote Originally Posted by Gildrein View Post
  1. When synthesis materials consist exclusively of normal items, the initial Quality will be close to zero. If all materials are HQ items, then the initial Quality will be around 500.
  2. When using Disciple of the Hand equipment and the appropriate abilities, Quality will improve during synthesis by 300 to 600 points.

(Example)
When all items are HQ items
Final Quality will be between 800–1,000 (odds of producing an HQ item range from 50% to 100%).

When all items are normal items
Final Quality will be between 300–600 (odds of producing an HQ item range from 0% to 10%).
* Actual figures are still under development. They may be adjusted or changed depending on feedback.
Pay special attention to bullet points 1 and 2.

1. tells you where you can expect your Quality value to be from the get-go based on whether you use all NQ mats or all HQ mats - 0 and 500 respectively.
2. tells you how much Quality gain an average person is expected to increase Quality during synthesis, provided they are well-equipped. The key here is this is a projection. Based on the rate at which they set Quality to increase, they are telling us how much we can expect to be able to increase Quality in the process of a single synthesis.

Now, the part you seem to be stuck on can be demystified quite readily. However it requires proficiency with a mathematical process known as Addition.

HQ mats: Start: 500 > Synthesis adds 300-600 > Result: [(500+300) - (500+600)] => [800-1,100].
They simply rounded this off at 1,000, which either means it's a Quality cap, or probably means at 1,000 you get HQ rate of 100% and thus no point in considering higher values.
NQ mats: Start: 0 > Synthesis adds 300-600 > Result [(0+300) - (0+600)] => [300-600]

The Quality ranges given are based on the values explained earlier in the post. Nothing suggests HQ mats give a bonus other than the initial 500 Quality.