I don't think it's usually permissible to remove legal liability for FDA approved treatments. Maybe there's some special arrangement here, but if the Comirnaty vaccine is completely unavailable then it hardly matters, because there will never be a Comirnaty vaccine injury, there will never be a Comirnaty claim for damages, and there will never be a Comirnaty court case. From that point of view it's a purely academic argument, and has no practical relevance in the real world. They know they can safely say what they like about Comirnaty and its legal liability, safe in the knowledge that there will never be any legal test case. Short answer, if they're lying, we'll probably never find out they were lying.
By the way, you should check out the relevant Federal Laws on Emergency Use Authorisations at uscode.house.gov (21 USC 360bbb-3: Authorization for medical products for use in emergencies)
(e) Conditions of authorization
(1) Unapproved product
(A) Required conditions
With respect to the emergency use of an unapproved product, the Secretary, to the extent practicable given the applicable circumstances described in subsection (b)(1), shall, for a person who carries out any activity for which the authorization is issued, establish such conditions on an authorization under this section as the Secretary finds necessary or appropriate to protect the public health, including the following:
(i) Appropriate conditions designed to ensure that health care professionals administering the product are informed-
(I) that the Secretary has authorized the emergency use of the product;
(II) of the significant known and potential benefits and risks of the emergency use of the product, and of the extent to which such benefits and risks are unknown; and
(III) of the alternatives to the product that are available, and of their benefits and risks.
(ii) Appropriate conditions designed to ensure that individuals to whom the product is administered are informed-
(I) that the Secretary has authorized the emergency use of the product;
(II) of the significant known and potential benefits and risks of such use, and of the extent to which such benefits and risks are unknown; and
(III) of the option to accept or refuse administration of the product, of the consequences, if any, of refusing administration of the product, and of the alternatives to the product that are available and of their benefits and risks.
Notice that in the last few paragraphs, people have to be appropriately informed of their right to accept or refuse administration of a product with Emergency Use Authorisation.
Appropriate conditions designed to ensure that individuals to whom the product is administered are informed-
(III) of the option to accept or refuse administration of the product, of the consequences, if any, of refusing administration of the product, and of the alternatives to the product that are available and of their benefits and risks.
I'd guess that means if Comirnaty is unavailable, then Joe Biden's vaccine mandate is unlawful.
Similarly, if people turn up for vaccination and are offered the Pfizer BioNTech vaccine, then failing to inform them that the product is on an Emergency Use Authorisation would be a breach of Federal Law:
Appropriate conditions designed to ensure that individuals to whom the product is administered are informed-
(I) that the Secretary has authorized the emergency use of the product;