Can a CSM deny orders for a leadership school such as BLC or ALC just because you don't get a 70 in each PT event?

Well if that E4 wants to make E5, why are they are a minimum standard looking to excel. They should be doing something to improve themselves physically and mentally. If they can't manage their fitness in garrison, how while they perform in a combat zone. We may be drawn down but stuff happens and you can find yourself back in the sandbox or on a 10,000 mountain looking at the other 3,000 feet above you. So yeah, the CSM will and should hold them back.

The short of it is, Most Soldiers that score 70 in each event have a hard time passing a APFT at the school house, the school house scores to standard and most units give there Soldiers the benefit of the doubt on exercises. It is to your benefit that you score higher and do not fail PT test at an NCOES. So just work harder and you will get there.

Ok. I am twisted here. I guess I always achieved to exceed the standard. If you wanna go and merely strive to meet the standard 60 in each event thats on you. Just know there are better Soldiers who deserve that slot.

As the Army saying goes you can add to but you can't take away from the regulations. Regulation states that 60 in each event is passing. But Commanders can enforce their own policy that states you must achieve a 70 in each event in order to attend NCOES. I personally agree with 70 for each event. I have seen Soldiers go to WLC barely passing their 2 mile run but they always passed. They get to WLC and have a bad day and fail by seconds. So to prevent this from happening the 70 point rule is enforced. Unless you have medical limitations a 70 in each event is not unreachable with a little work. And it saves you from potential getting a Marginal on your 1059.

By regulation? NO, in reality and by functionally effectiveness, you bet.

They can deny anything they want. But that would mean it's either personal or they are just being a prick! ( IMO)

Looking at the Prerequisites for attendance for Maneuver SLC. If a Solider fails the APFT (twice) they are removed from the course. The consequences of being are outlined in the hyperlink. Now a soldier who earns 60 points on each event passes the APFT according to regulations, but is that Soldier, especially a NCO living the Creed and Army Values? I would argue that the CSM is this instance is exercising excellent judgment in not allowing this NCO to attend PME until that NCO demonstrates "excellence in Physical Fitness" and not just enough to meet the standard.
On a personal note, once upon a time when I was a PLDC instructor, ever Soldier who showed up to attend the 101ST NCOA had "passed the APFT" within 30 days of attending. The APFT failure rate was so high, that we had a vide camera operator standing by. A grader would signal a Senior Instructor who would stand next to the grade and observe. If needed the senior would signal the video camera operator who would video the soldier performing the Push Ups and or Sit-ups. If the Soldier failed the APFT, the video was shown the PLDC 1SG. It was an unbelievable set of checks and balances, but the amount of APFT failures from Soldiers who had "passed the APFT recently" was equally unbelievable.
Just my perspective from my Mortar Pit.

** ATRRS Prerequisites and consequences for failing the APFT**
https://www.atrrs.army.mil/atrrscc/prerequisites.aspx?fy=2014&sch=698&crs=0-11%2F19-C46&phase=1&cls=003&clsflag=&startDate=2014-03-04&endDate=2014-04-07

Yes he can. And really he's not doing it cause he doesn't think it'll shine upon the battalion good or anything like it, it's more of he wants to ensure you'll pass your APFT at the school and perform well. He doesn't want to send someone and then they find themselves out of the school cause they couldn't pass the APFT.

Can and should just to save you from yourself and failing.

I feel that he or she should not hold you back unless, you barely made it.