The truth is…
According to Robert’s Rules of Order Newly Revised 12th Edition the following information indicated by the section symbol “§” is true unless the organization has adopted a rule to the contrary.
§4:3 After debate begins or any member voted, the lack of a second becomes immaterial and it is too late to make a point of order the motion is not seconded.
§4:11 Motions listed as requiring a second do not need to be seconded when made by direction of a board or committee.§4:12 If the chair is certain a motion meets with wide approval, but members are slow in seconding it, the chair can state the question without waiting for a second.
§4:13 In handling routine motions, less attention is paid to the requirements of a second. If the chair is certain that a motion meets with wide approval, but members are slow in seconding it, the chair state the question without waiting for a second.
§4:14 For lists of certain parliamentary motions that do not require a second, see pages t44–t45.
§5:6 …most of the motions in this latter group do not require a second (see pages t44–t45).
§12:91 Regardless of whether the maker of the main motion "accepts" the amendment, it must be opened to debate and voted on formally and is handled under the same rules as amendments generally.
§4:19 After the question has been stated by the chair, the motion becomes the property of the assembly, and its maker can do neither of these things without the assembly's consent…
§17:14 It is out of order to move to lay a pending question on the table if there is evidently no other matter requiring immediate attention.
§17:15 The motion to Lay on the Table is often incorrectly used and wrongly admitted as in order with the intention of either killing an embarrassing question without a direct vote, or of suppressing a question without debate. The first of these two uses is unsafe if there is any contest on the issue; the second is in violation of a basic principle of general parliamentary law that only a two-thirds vote can rightfully suppress a main question without allowing free debate.
There is no such requirement in Robert’s Rules of Order Newly Revised.
If someone alleges there is such a rule have them state the rule, by giving the section and paragraph number to verify the rule.
There is no “three reading” requirement in Robert’s Rules of Order Newly Revised.
There is in the Standing Rules of the Senate of the U. S., Rule Number 14, clause 2.
There is in the Rules of the House of Representatives of the U.S., Rule XVI, clause 8.
There is in Mason’s Manual of Legislative Procedure, §720, p. 490.