That publication isn't teaching pilots anything as it's not targeted to pilots. It also does not say "VFR pilots must receive 'cleared into the Class Bravo'." It says, "VFR aircraft must obtain an ATC clearance to operate in Class B airspace." Which is correct because
all aircraft must obtain an ATC clearance to operate in Class B airspace. Here is the regulation:
§91.131 Operations in Class B airspace.
(a)
Operating rules. No person may operate an aircraft within a Class B airspace area except in compliance with §91.129 and the following rules:
(1)
The operator must receive an ATC clearance from the ATC facility having jurisdiction for that area before operating an aircraft in that area.
(2) Unless otherwise authorized by ATC, each person operating a large turbine engine-powered airplane to or from a primary airport for which a Class B airspace area is designated must operate at or above the designated floors of the Class B airspace area while within the lateral limits of that area.
(3) Any person conducting pilot training operations at an airport within a Class B airspace area must comply with any procedures established by ATC for such operations in that area.
(b)
Pilot requirements. (1) No person may take off or land a civil aircraft at an airport within a Class B airspace area or operate a civil aircraft within a Class B airspace area unless—
(i) The pilot in command holds at least a private pilot certificate;
(ii) The pilot in command holds a recreational pilot certificate and has met—
(A) The requirements of §61.101(d) of this chapter; or
(B ) The requirements for a student pilot seeking a recreational pilot certificate in §61.94 of this chapter;
(iii) The pilot in command holds a sport pilot certificate and has met—
(A) The requirements of §61.325 of this chapter; or
(B ) The requirements for a student pilot seeking a recreational pilot certificate in §61.94 of this chapter; or
(iv) The aircraft is operated by a student pilot who has met the requirements of §61.94 or §61.95 of this chapter, as applicable.
(2) Notwithstanding the provisions of paragraphs (b)(1)(ii), (b)(1)(iii) and (b)(1)(iv) of this section, no person may take off or land a civil aircraft at those airports listed in section 4 of appendix D to this part unless the pilot in command holds at least a private pilot certificate.
(c)
Communications and navigation equipment requirements. Unless otherwise authorized by ATC, no person may operate an aircraft within a Class B airspace area unless that aircraft is equipped with—
(1)
For IFR operation. An operable VOR or TACAN receiver or an operable and suitable RNAV system; and
(2)
For all operations. An operable two-way radio capable of communications with ATC on appropriate frequencies for that Class B airspace area.
(d)
Other equipment requirements. No person may operate an aircraft in a Class B airspace area unless the aircraft is equipped with—
(1) The applicable operating transponder and automatic altitude reporting equipment specified in §91.215 (a), except as provided in §91.215 (e), and
(2) After January 1, 2020, the applicable Automatic Dependent Surveillance-Broadcast Out equipment specified in §91.225.
[Doc. No. 24458, 56 FR 65658, Dec. 17, 1991, as amended by Amdt. 91-282, 69 FR 44880, July 27, 2004; Amdt. 91-296, 72 FR 31678, June 7, 2007; Amdt. 91-314, 75 FR 30193, May 28, 2010]
Note that the Part 91 airspace regulations, 91.126 through 91.135, are found in the General Flight Rules, not the Visual Flight Rules. They apply to all operations. If the regulation was followed as written
every aircraft, IFR as well as VFR, would receive a clearance from the facility that owns the airspace prior to entry.