You're absolutely right, though given the choice between developing a large scale app with SQLite or MySQL I'm afraid I'd go with SQLite. At least I'd know what hell I've wandered into.
We are in danger of encouraging a small war here, but I would partly agree with you in that I would not by choice use mySQL for anything. IMO there is nothing for which one of SQLite or Postgres (or SQL Server or other decent RDBMS) are not more suitable for. mySQL and its descendants/variants are popular today mainly because of a mix of two things: many people not knowing better and its popularity having significant momentum.
I still wouldn't use SQLite for a large scale app (assuming that means one that needs concurrent data access for multiple users) though: it is not the right tool for that sort of job.
Definitely not in the same category: the goals for SQLite are very different to those of MSSQL and Postgres.
It is impressive how well SQLite performs and scales so you sometimes see it do the job of a "larger" engine because a project accidentally grew and hasn't been re-factored in that respect yet, but if you are starting a new project I can't think of any cases where you would ask yourself if you should use it instead of MSSQL/Postgres. For an integrated storage engine for your app with SQL semantics, ACID, and so forth: SQLite wins hands down. For a fuller database and anything that needs any significant concurrency SQLite is not what you want and isn't trying to be that.