You don't seem to think dynamic method invocation is wrong, but using constants the same way is? Again, that would be ridiculous IMO.
You are so sure of yourself Ree I almost starting blinding agreeing with you. I didn't and that's because, mostly, I don't

and for this reason I think you should pay attention. A disagreement is the genesis of realization (for somebody), providing an agreement can be reached ultimately and the debate's potential merits are not outweighed by the amount of time required to obtain them. With that in mind: -
A method represents a unit of behaviour. To choose the behaviour you wish to use dynamically improves flexibility. Simple. Despite this, calling method dynamically usually implies the use of __call() and is not always a good idea. There are issues of poor reflection. Documentation becomes more complicated and obtuse. Code readability and predictability usually suffers; this is in part redeemed by accepted practise e.g. design patterns.
The most legitimate use of a dynamic method invocation is direct delegation. Here the use is obvious and easy to explain and can be seen in certain implementations of the decorator pattern. Even with its drawbacks dynamic method calling, class instantiation and loading often provide advantages that are significant enough to justify their use.
Using a constant ensures that the correct value is being used and improves readability. I'm sure you are aware that if you attempt to access a constant that does not exist you will get an error. The dynamism makes no sense because where you had ensured integrity and predictability you are now throwing it out the window by creating the risk of attempting to access a constant that doesn't exist or accessing the wrong constant in the same way that using no constant at all puts you at risk of using incorrect data. In addition to this you can no longer see the name of the constant you are calling because that name is being generated dynamically. One could say that calling a constant in a dynamic way is negating the purpose of a constant altogether. Whilst there may be times where this certain combination of advantages and disadvantages makes more sense then any other I am willing to bet it is infrequent enough that I should question your use of it.
I would be interested to see your code Ree.