How can a career soldier be threatened with involuntary separation for one ftr?

IF everything is as you said and there is no other extenuating circumstances ... they can't. The unit commander and admin folks would know this (or should know it) so that's why I emphasized the "IF".

What's the rest of the story? Are there additional disciplinary issues? Was the "one time late" involving Annual Training and they "eventually got there"? Was it a movement (deployment)?

IF there is nothing else behind the scenes that isn't being mentioned, first, they need to address this with their unit commander to ensure there is a common understanding of the circumstances. IF the situation is as still stated, then contact the state's IG* (as you are ARNG, I assume the Soldier in question is in the ARNG) as they are clearly not following regulatory guidance.
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* ARNG Inspector General website - https://www.nationalguard.mil/Leadership/Joint-Staff/Personal-Staff/Inspector-General/

References:
● AR 135-91 (Service Obligations, Methods of Fulfillment, Participation Requirements, and Enforcement Provisions) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN8277_AR135-91_Web_FINAL.pdf
● AR 135-178 (Army National Guard and Reserve Enlisted Administrative Separations) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN43322-AR_135-178-000-WEB-1.pdf

SGT Bruce Chapman , COL Randall C. provided the typical scenario. Usually, there is something else going on. More details needed, and I am not saying this is not the unicorn story of "a totally innocent Soldier getting screwed by the Army who did absolutely nothing wrong and had an exemplary military career, but was late for the bus to Annual Training".

However, I will say, the CDR can *initiate* separation for anything. Whether it gets past the BDE CDR or not is a whole different story. Usually, FTR is easier to get through, especially when combined with minor offenses such as failure to maintain security clearance, failure to attend BA, repeated ACFT failure, and failure to maintain compliance with ABC, failure to adapt, malingering, etc; especially if there are little to no written records.

On a side note, I had a CG once who would call every Soldier with an FTR separation request and get the soldier's story (or the DCG would). I would say the number of times the Soldier was retained was not insignificant. It really indicates a failure from subordinate CDR's to do their due diligence.

Did the Soldier miss a PT formation, or miss movement?