Big picture preface: I absolutely agree that you know your child better than any professional who doesn't live with him, and that you should do whatever makes the most sense for your family to give him both the challenges and supports that he needs to develop according to his own needs.
As someone who has given these evaluations to children with developmental delays (and there is a reason the developmental delay category exists--so that children with genuine delays, not "delay" as an euphemism for long-term impairment, can receive needed interventions without a permanent label), I've generally tried to convey evaluation results in very young children as "state" rather than "trait". IOW, this is where this child is functioning right now, under standardized conditions, which has implications for their service needs -right now-, but shouldn't necessarily be viewed as locking in their long-term trajectory. At just five, federal special education regs allow for remaining under the developmental delay category. It may be that your state ends the use of that category on his fifth birthday, which is why they may be introducing a new disability classification.
The determination of a disability must be based on multiple measures, so certainly, it is legitimate to ask what the other available data, outside of the cognitive, says about the appropriateness of intellectual impairment as the disability. Presumably, other data was collected.
As to catching up...it is not uncommon for children on the autistic spectrum, and children with communication disabilities, in particular, to test much lower early on than they do later in childhood or in early adolescence. I routinely see ASD students whose historical cognitive numbers show a steady rise from their preschool assessments through the last assessment I give them before they leave high school. Some have dramatic rises of multiple standard deviations. These aren't the only two disability types that have these kinds of changes. The big picture is simply that very young children don't have very testable behavior, and therefore don't have very stable test results; it's easy to low ball them.
At the same time, keep an open mind about the current value of the testing data. These tell you how your child performs under standard conditions; school is full of standard conditions, so there is relevance to performance in the conventional school environment. Of course, you spend much more time with your child, and your relationship is such that you are both more alert to his demonstration of skills, and a safer environment for him to display those skills. That's normal, and good. But it doesn't mean his failure to demonstrate those same skills on-demand for a relative stranger should be discounted.
And please don't be discouraged by this, but objectively, I should note that most of the skills you've listed are memorization-related skills. I'm not saying that he doesn't have more abstract problem-solving skills, but the specific academic-related items (knowing letters, numbers, colors, shapes, and memorizing tunes) named could all be explained by a strong rote memory, which is not incompatible with low cognition. Nor is being able to effectively manage his social environment to get what he wants.
The reality is, development can take many different twists and turns, so that what he needs right now for educational interventions may not be what he needs in the future. How he presents now may not be the whole of how he presents in the future. And how we define ability can be much narrower than the true scope of human giftings. He may have academic and/or intellectual challenges, and yet also have musical and interpersonal gifts. Or he may have cognitive gifts too, but obscured by other challenges. Regardless of how his "true" learning profile looks, he is certainly always capable of learning more, and of benefiting from expectations that move him to the next level.
And on a side note, even individuals with IQs in the 50s can be functioning adult members of society, living happily and independently on a day-to-day basis, and holding meaningful employment and relationships. They are very far from vegetables. (I know you didn't mean that literally, as in a vegetative state, but I just wanted to clarify this for the record.)
