It could be. If you are not having problems where you have to make repairs to this area, then do not worry about it. From what I understand if you don't disturb the asbestos you are ok. It's when you cut into it or it becomes frayed, etc that you may have problems. If this bothers you, you should also be able to cover it up (some sort of paint or wrap).

"The basement is filled with 8x8 vinyl floor tiles" Asbestos can be absorbed when it becomes "friable", IE. airborn and there are methods to deal with it, which are user friendly. RE the basement floor; Both the adhesive and the tile can contain asbestos. There is a simple method that easily defines what you have. Remove a portion of or a whole tile exposing the glue. Pour a small quantity of boiling water on the adhesive. If the adhesive bubbles and loosens, IT IS NOT CUTBACK, if it does not, it is, and your option become substantially narrowed. The probability of your patio and basement walls having asbestos been used as a binder is highly unlikely, given the era of the construction. The product in the bathroom pictured appears as normal asphalt impregnated water resistant material of that era.

The fibrous "stuff" looks like an acoustic product in panel form, the name of which escapes me. First I thought it might be moisture-compromised (exploded) particle board, but it sure does look like that acoustic panel. BTW, acoustic panels of the type I mean we're never intended to be used as flooring underlayment.

If you are worried, get it tested. As is, if there is asbestos in it, it's not going anywhere being bound up in adhesive. So you could paint it to further encapsulate it and install new base over it.