I don't recognise that interpretation of the model and it doesn't seem to make sense to me. For example if you start at the "Low Cost" corner and move to the right you are saying, effectively, "it will cost more and more as you move to the right but you will deliver it quicker and quicker"...
The point of the triangle, in my view, is to highlight the relationship between three critical "levers"; Time, Cost and Quality. Where your project "sits" within the triangle (yes, including in the middle), demonstrates the appetite of the project board, or the sponsor, or the company etc. to assign relative importance to the levers.
For example, if your project is right against the Cost corner, then it is saying that sticking to budget is the absolute most important lever. The relationship of the corners of the triangle means that if you absolutely prioritise one of the corners over the others you must, by definition, deprioritise the other corners. In practise, if you must stick to the budget against all the odds, you cannot also enforce rigid compliance with timescale or quality metrics.
If you absolutely must stick to a timescale, then you cannot restrict the budget or the quality and if you prioritise Quality as paramount then you cannot restrict the budget or the timescale.
In the real world, projects exist within environments that comprise a mixture of priorities of these three levers- rarely is one of them at 100% (meaning the others must be zero) so the dot representing that project would live somewhere within the boundary of the triangle. This is entirely normal.
If you ascribe other meanings to the corners then the meanings will change, but I believe what I have described is the classic Project Management meaning of the triangle.