It's still a national competition and, to my knowledge, has nothing to do with the size of the unit. There are a certain number of sideload 3 year and 2 year scholarships set aside for each class year. For example, for class of 2015 there are 80 3 year scholarships and 108 2 year scholarships have been set aside. So there are not many scholarships available in these times. I have no idea what the numbers might be for class of 2016. Your guess as to the number of people competing for these is as good as mine, but I'm sure the LT was making a valid point.
There are many advantages to participating as a College Programmer, hence my remarks. You bond with the other folks in the unit, especially the freshman during orientation. You learn time management out of necessity. You learn leadership skills and discipline. All these can be useful in making the college transition. I know my DS is far exceeding his performance in high school and my own expectations for him. I have no doubt this is due to his NROTC participation without the scholarship. YMMV. However, his participation does not assure him a commission. He will need to be awarded Advanced Standing in his rising junior year if he is not awarded a sideload scholarship. Advanced Standing will win him a monthly stipend and the privilege to continue in the program.
All ROTC participants are treated the same. Scholarship or not, they all get the same opportunities and demands for performance. There is no path thru NROTC that guarantees a commission without hard work and dedication. Some are disenrolled for failure to meet the standards. Some leave voluntarily.
Not sure how to guide you in making a decision. Clearly $ are important in obtaining a college education. My DS was lucky to obtain a merit scholarship that allowed him to attend his #1 choice school for near in state tuition. He has to maintain a 3.0 to keep the scholarship which is more demanding than the NROTC GPA requirements. Some schools offer in state tuition for ROTC participants. The alumni of some units offer financial aid for tuition for college programmers. Some schools offer room and board. It all varies by the unit/school. You might try contacting the units at schools he is accepted to, or their financial aid offices, to see if there is anything that can be done financially for a college programmer. Certainly apply for any scholarship for which your son is eligible. It may be, given your financial situation, that following the LTs advice might be your best option.
Good luck to you and your DS. I hope his dreams come true.