About removing things from your report, they are actually lying to you. There is no law anywhere requiring anyone to report your bad credit, and there is no law saying they can't remove the report.
Unfortunately, as things stand, you are going to be stuck with the listings.
If you ever have another collection, however, there is a way to get it off your report. As you already know, collection companies always offer to "settle" for something less than the full amount. What you need to do is offer to pay the full amount if they will agree to completely remove the entry from your report. This costs you more, but you get the thing off your report, and a judgment is the only kind of account listing that is worse for your credit than a collection, whether it's paid or unpaid.
The collection company, doesn't really care what happens to your credit. They're in the business of making money. They see the credit report listing as a tool to force you to pay, not as some kind of necessary and deserved punishment. By offering full payment instead of a settlement amount, you are offering them more money, and their entire purpose is to collect as much money as they can, with as little effort as possible, on each debt that they handle.
One problem can be that the people who work the phones do not understand this. In fact, many of them really do think it is illegal to remove something, or think that it cannot be done. If you run into this, you just have to get yourself passed up the supervisory chain until you reach someone who actually has the authority to make this kind of a deal. Believe me, that person DOES exist in every single collection company.
If you do make a deletion in return for full payment deal, make sure you get it in writing before you pay, that it mentions a time frame and exact amount, such as "immediately upon receipt of verified funds in the amount of $XXX.XX", and that it says specifically that they will delete the "collection account" from all credit reporting agencies to which the collection has been reported, not that they will delete the "trade line".
Since you seem to have already paid your collections, it is too late for this kind of a deal. What you CAN do is make certain that they drop off your report when they are supposed to. Assuming that the collection agencies you dealt with were working on behalf of the original creditor, as opposed to working for, or themselves actually being, new owners of the account concerned, the Date Opened, Date of Last Payment, Date of First Significant Delinquency, Date of Last Activity and Date Closed all have to match the dates from the original account. Collection companies will sometimes change these dates, using things like the date they first started working on it as the Date Opened, or the date that you paid them as the Date of Last Payment and Date of Last Activity. Make sure all those dates are correct because they govern when the collection will drop off your report.
Handy Tip: If a dispute to the credit bureau does not get these sorts of incorrect dates fixed (the collection company only needs to tell the bureau that the listed dates are right - they don't have to prove it), write to the original creditor. Ask when was my account opened, when did I make the last payment, when did you close it, etc. When they respond, you can use their letter as proof that the credit bureau will legally have to accept.