Being in the elite field and being invited are two entirely different categories.
There are maybe 30 or so invited runners, maybe a handful more. But having the elite start does not mean you were invited. It just means you're among the top 60-75 runners and therefore will be given a few more accommodations.
For instance, you can be a male elite runner if you run say 2:23 as a qualifier. But you will not be invited and you will not receive any special treatment above pre-race space in the church. Perhaps you may also receive entry into the Fairmont for a post-race massage. But even in the church, you are going to be relegated to a common area of the church. You won't get a special room for just yourself and your group, like Meb, Desisa, or some of the invited elites.
More proof LHG was not invited - her name was not on her bib. She is just F119 in photos. The top seeded master, F101, Nuta Olaru, is. F104, Gruca has her name on the bib too. It appears that the bibs with names ends at F106 - Davenport.
What really happened Monday (and the leadup to it) is that Liza was admitted into the race and whether the BAA's policy is to not allow former suspended runners into the race, or they just missed it during registration, we will likely never know. This will all be forgotten about very quickly.
LHG was not expected to finish top 3 (let alone win the division) and ... she did. Keep in mind, the winning master's time in 2014 was 2:36, then 2:37; 2:41. Those results are consistent with 2013's winning master's times as well. This year, LHG's time this year was a 2:48. I strongly doubt the BAA thought that she would win the division when she registered and that may be why she could have been overlooked as a registered competitor.
Now the BAA is faced with two prospects: deny her prize money and face a lawsuit. Or, pay her and take whatever PR hit there is and make sure any lapse (if there was one in the first place) does not happen in 2016.