Sure, unless you're talking about the series or movie pitch that you've spent weeks or months developing. But that's exactly what can happen if you don't follow up a meeting with a written version of your pitch.
Frankly, I have NEVER understood a writer coming in to pitch a project without having something down in writing. Hello! At the end of the day, we're hiring you to write a project, not verbally tell a story. Unless you've got a list of credits as long as your arm (and frankly, if you did you probably aren't reading this blog), you're going to have to prove you can write the characters and situations you've described at some point. Allegedly writing is what you love to do and what you do better than anything else so why not show it? But I digress...
So you meet with the producer, development executive or agent. You tell the best story ever, with characters that jump to life and a line or two of really smart dialog. Guess what happens next? The person you pitched it to has to pitch it to the next person up the food chain. Always. There's always a bigger fish who has to weigh in on whether or not to pursue your project. Seriously, I don't care who you've pitched to, they have to sell it up the ladder to the producer, the studio, the network, the talent. Sometimes all of the above. Are you willing to bet your project that they get every nuance of the story and character right as they orally pitch this from one desk to the next?
Even with the best of intentions, often times the spirit and tone of the piece can get mangled. Everyone has days when they're in a crappy mood or hate their job or got dumped by their girl or took a decongestant... whatever the cause, no one pitches every story perfectly every time. Hedge your bets and help the person who is trying to help you by giving them a written form of your pitch.
WHEN AND WHAT TO LEAVE BEHIND:
Generally speaking, it's best NOT to leave behind pages or a synopsis at the end of the meeting because you'll want to tailor your idea based on any questions or concerns that came up in the meeting. At the very least, pretend you are going to do that.
Before you leave, without being pushy or rude try to get the executive's e-mail or their assistant's so you can follow up the meeting with a BRIEF synopsis of what you pitched to them directly. And I do mean brief. Something that can easily be passed along in an e-mail is best, so try limiting it to a page or page and a half. Giving them a catchy, memorable logline to boot is icing on your cake.
ETIQUETTE TIP: Get an e-mail or an address of everyone you meet so you can follow up EVERY meeting with a polite "thank you for your time, it was wonderful meeting you" note. It makes a difference.
Someday, after you've pitched your idea but no one sees the genius of it all, it may be necessary to spec the script out. That means writing it on the speculation that someone will buy it once they see the idea on the page. A lot of movies and series have gotten set up that way lately, even from newbie writers so don't dismiss the idea as ridiculous. Again, you love to write, you want to sell this... maybe I'm a dolt, but I don't see the problem.
Seriously, you want to be a writer so prove it by writing. Whoever tells you not to write a word until someone pays you for it isn't doing you any favors at all.