I don't mind pressure situations, where something must be done quickly with lots of people asking/watching. However some people don't handle those well. I'm not sure I'd classify them as useless. They wouldn't be good in those situations, but if those aren't a daily occurrence, or they don't require everyone's help, there are plenty of uses for people that don't work well under pressure.

I would agree that someone that lies about their schooling, projects, or something specific should be let go. However I think those situations are few and far between. Often someone exaggerates their contribution. Trying to pin that down specifically can be hard, since exaggeration is a subjective thing.