You are missing the term "ATHLETIC AID". Not need based, Not academic, Not a grant from the Irish American club but "ATHLETIC AID" or "ATHLETIC SCHOLARSHIP" is the key.
I'm not sure you really understand the nuances of the NCAA rules - which admittedly can be confusing and have some grey areas. In a past life I once worked in this area and I understand them quite well. I fully understand that the issue is ATHLETIC AID. What is unclear is whether that is what Pulido is receiving. I can find no evidence as to what kind of aid she is getting or whether it would be classified as "athletic aid" under the NCAA bylaws. It is irrelevant that she is an athlete - only the
type of aid matters. A few facts:
1. As a track athlete, if she received either normal need-based aid or some sort of earned academic scholarship, that is NOT "athletic aid", per the NCAA bylaws, and that would not make her a "counter".
2. The great majority of track athletes do not receive full scholarships (or even half) since the number available is very low relative to the number of athletes on a team. Thus schools try to use need-based aid and/or academic awards as much as possible, since that money does not count towards the scholarship limit (except in sports such as football and basketball). Pulido was a good, but not great, recruit - and UConn brought in 17 T&F athletes her freshman year, some clearly better than her. There were likely about four athletic scholarships to split among those 17 athletes, so it is clear that the coaches would use other types of aid as much as possible, as many programs do.
3. I don't know - nor do you - how her aid was structured. And newspaper articles are unhelpful since 99.9% of writers have no understanding at all about this subject. For an example of that, spend some time looking at articles over the years on Ivy League and Patriot League (pre-2013) football recruits. See how many of them supposedly got scholarships - even though neither of those leagues allows its members to give scholarships. All these players received was need-based aid, which the writers confused with a football scholarship.
4. IF she is now only receiving need-based aid and/or academic awards, then as a basketball player who was not recruited, she would not be a counter for basketball. Again, neither of has any idea - and she certainly could be a counter. But I can find no evidence either way as to what kind of aid she is receiving or how much.
5. To repeat, she may well be a counter. But I have seen no evidence, either way, to make a judgement.