There is still an API limit, Andy just meant that it’s separate from the 2,400 per user daily account limit. The API limit is 15 tweets per user per 15 minute interval, spanning across all 3rd party applications as per https://dev.twitter.com/rest/public/rate-limiting.
Also note that there are finer levels of that limit of 2,400 per day, meaning that you can’t tweet 2,400 times all at once, there’s a finer limit of 100 per hour. You can probably break it down further than that to determine a reasonable maximum per minute (although I haven’t verified or seen this).