Up to now the word session has included many different types: Music, Song, Poetry, Story Telling etc. These major categories can often be broken down further. For instance song could include: Shanties, Ballads, West Gallery/Sacred Harp etc, and music could be split into Irish, Scottish, English Country Dance Band, Bluegrass, Morris, etc.
My feeling is that it is Pied Piper who is trying to hijack the word - probably to fit a very narrow band that happens to be his own personal interest.

Provided that the content and aims of a session are declared, then anything which fits into the stated range is admissable. If you don't want singers in your session, then make it clear from the start - they'll go somewhere else. For example the session which happens once a month near Southwark Street is specifically for English Country Dance Band music. Personally, I prefer a well run mixed sessions like some of the ones we manage at The Moreton Village Festival.

My pet gripe about sessions is the need some people seem to have to play tunes they know everyone else cannot join in with...
If you only have tunes that everybody is capable of playing, the session will soon become boring and stagnant. Perhaps you won't be able to play along first time, but if you like the tune enough, you'll soon learn it and thus increase your repertoire. Part of a session should be listening to other people performing, sometimes so other members can learn something and sometimes to give less experienced members a chance to play something themselves without getting drowned out by others.

Song sessions do tend to be different. Most singers would expect to sing the verse on their own rather than with every joining in, although participation (unison or harmony) in the chorus is usually welcomed. Instrumental accompaniment should be at the discretion of the singer. If a singer has a quiet voice a crowd of melodeons, fiddles, and bodhrans will probably completely drown them out. If accompanying musicians are sympathethic to the timing, phrasing, and nuances of the singer, they can be a great help, but many times they want to play at their own speed and rhythm all the time. If Pied Piper would like to hear just how sensitively a whistle player can accompany a singer, he should try going to a session with mudcatter "Leadfingers" around (how about that I'm complimenting you Terry).

Incidently, when I choose to sing a song unaccompanied, it's because I want it that way - not because I can't play my own backing.