It is correct. Most shared hosting companies limit the outgoin mail per domain per hour.
You need at least a VPS. Be sure to ask your VPS provider if he allows mailing from his servers, and be sure that your subscribers emails are collected directly from their owners. Most hosts will suspend your server or send you a warning if they receive any spam or abuse complaint.
Thanks all for your answer. I will look for VPS offers.
Just one question, how can hosting campany suspend the account ? They verify number of emails sent/day ? or the bounce email ? or complaint from members ? or how it works ?
As mentioned, many shared hosts limit outgoing email to as low as 80 per hour (some are at 300 an hour). On a VPS, you can configure the limit to "unlimited" which will allow you to send email at the speed the hardware (server and port) will allow.
I think you would want to space out the emails using a program such as PHPList, sending the email to a portion of your list each day. You could set it at 1,000 per hour and take a few days to send the email, and that probably would not overload your server. In any case, talk to the host about it.
Your VPS will have its own IP address, not shared with anyone else, so you are more likely to find a host willing to allow this with a VPS. That size list is really a candidate for a commercial email service like Constant Contact, MailChimp or others, but that can get pricey.