I think It's allowed to send more than 2 PM's in one day but limited to 5PM's per hour check this quoted below posted by our admin.
I've adjusted the limits to make spamming more difficult.
| Activity | Min. seconds between post actions | Max PM recipients | PMs per hour |
| 0 | 360 | 3 | 5 |
| 16 | 74 | 5 | 30 |
| 30 | 60 | 5 | 60 |
| 60 | 30 | 5 | 60 |
| 100 | 12 | 10 | 120 |
| 200 | 10 | 15 | 120 |
| 300 | 8 | 20 | 120 |
I hope that the above quoted could help you to get an idea.
Anyway, upgrading to copper member could increase your interval limit for pm's and posts.
You posted outdated quote. Few months ago theymos updated PM limits, here is link to his post:
If OP will purchase Copper Membership he will be able to send up to 40 PM's per hour/ 120 PM's per day.