TSA advises passenger by phone they need minimal or no ID

Two reports lately indicate that TSA is telling travelers who inquire by phone that they can get by with minimal ID. This is a bit strange, because in my experience, the TSA either wants to see proper ID or no ID at all, and misleading because, of course, you don't need any ID at all. However, it is better than the old days, when TSA seemed even more confused about ID.

Adeline reports that Delta wouldn't give her a boarding pass without an ID, even though she had alternative ID. However, TSA was pretty clear with her over the phone that, as far as they are concerned, they just need a boarding pass. As Adeline found out from the TSA, she doesn't actually need any ID. Delta has strict rules about ID for the sake of thir own revenue control--they don't want you buying someone else's ticket. Of course, this it their right. However, a traveler can check in online and print their boarding pass, or print it at a kiosk. This may mean no checking any bags (depends on the airline). However, once you get that boarding pass, you are free to travel. Even the strictest airlines, like Delta, will usually give you a boarding pass if you can provide them of enough evidence of who you are, so I am surprised they are being so hard line about it. Adeline writes:

So all I had was my BYU ID, and [Delta] didn't accept that because BYU is a private institution so the ID is not issued by the state. The dumb part is that the agent would have issued me a boarding pass if I had a library card. A library card? It has no photo, it is easily stolen, and is easy to get. That really didn't make sense to me. And yes, I did cry at the airport. She still didn't give me that little piece of paper. She did however transfer my flight to tomorrow night, free of charge.
So I went home and stripped my room to look for my license while sitting on hold with Delta Airlines and then TSA for an hour to see what forms of ID I could use to get on the plane tomorrow. Let me preface this by saying that I understand that it is a federal law that they can't give me a boarding pass without proper ID. The problem is that no one knows what proper ID is. This is how the 3 separate phone calls went:
1) The first lady said that I could use my library card and she said that her supervisor told her that he was 80% sure that my International Student Identity Card would pass through an agent, but that I should call TSA to make sure.
2) TSA didn't help me because they said you can pass through security with practically no ID as long as you have a boarding pass. They just do a secondary screening.
3) The third lady (back at Delta) said that I couldn't use my International card and that I couldn't use a library card and that the agent that said I could was just being nice.
So if the agent wasn't "supposed" to let me in with a library card, then why couldn't she just let me in with a BYU photo ID (which is harder to fabricate and cannot be used in someone else's name)?

Epenshade reports that relatives "were in a panic about how she would get home since she had no ID" when a purse was presumed stolen:

As Ty put Elise to bed, I pulled up the TSA phone number and called them to see how she could get home. They were very kind, and told me with a police report she could fly, but she would be subject to additional screening. When I called her back to tell her this, she seemed a little calmer.

Why is TSA saying they require a police report to fly without ID?