Yes, im a Kindergarten teacher working in 4 year old sessional kindergarten with a background in childcare- currently on maternity leave. Yes your idea sounds reasonable. It's unlikely she would do a poo at kinder and might wait until she gets home.
I'd encourage you to request that they change her still though. It is part of their job. Sometimes the 'expected' line is used by some staff because of facilities or because they just don't want to be changing nappies/ pull-ups... almost a snobby thing.
I'd ask them why it's expected, especially in 3year old kindergarten.
On the 'lying'... It's very normal at this age and beyond for children to lie. It's a vital part of brain development and shows a level of maturity vital for self preservation and living in a social world.