The help center article is actually fairly accurate. The details you found in Shog's answer are just the criteria that cause the profile to get held up for review before the profile deletion goes through. They are not actual criteria for whether the votes get preserved.
The actual criteria on whether the votes get preserved is a bit more complicated - whether or not that profile has engaged in any illegitimate voting behavior in the past. There are a lot of things to look at when considering that factor. Generally speaking, a higher reputation user is more likely to pass that check without issue, whereas a lower reputation user is likely to face much more scrutiny. After all, a huge number of votes is less suspicious from a higher reputation user.
Also, consider some data. Historically, most users who are involved in some sort of voting misbehavior rarely ever go on to actually be very high reputation users. Either they give up and stop using the site or have their profile deleted. For example, here is a reputation breakdown of all the users on Stack Overflow who still exist on the site that have been contacted for either targeted voting or sockpuppet upvoting at some point in the past:
Reputation Range | Number Users Messaged
< 1000 | 5,035
1,000 - 4,999 | 970
5,000 - 9,999 | 127
10,000 - 49,999 | 73
50,000 - 99,999 | 2
100,000+ | 3
Note: This data excludes all users whose reputation was 1 at the time, because they could have been suspended and not actually have a reputation of 1. It of course doesn't include now-deleted users because I don't know of a way to easily get previous reputation of a deleted user.
So without going into all the fine details in the help center, the current text is pretty spot-on. Simply having a high number of votes cast is not the sole indicator on whether the votes will be preserved, so it required something extra to indicate that. Thus reputation is used, since a very high reputation is the best simplification of the criteria that secondarily determines whether votes will be preserved, based on how often it occurs.