Even banks get confused about PMI cancellation. To my surprise, my bank automatically removed PMI when we hit 80%, without an appraisal, and they even said we didn't need to request it. As for Google searches, it's like people are playing the telephone game, where they interpret what they read on another web site.
Here are the relevant sections of the law. First, they define the "cancellation date" based on reaching 80% LTV.
(2) Cancellation date
The term "cancellation date" means -
(A) with respect to a fixed rate mortgage, at the option of
the mortgagor, the date on which the principal balance of the
mortgage -
(i) based solely on the initial amortization schedule for
that mortgage, and irrespective of the outstanding balance
for that mortgage on that date, is first scheduled to reach
80 percent of the original value of the property securing the
loan; or
(ii) based solely on actual payments, reaches 80 percent of
the original value of the property securing the loan;
(Mortgagor means borrower.) Then, they define the "termination date" based on the originally scheduled date to reach 78%, not based on actual balance.
(18) Termination date
The term "termination date" means -
(A) with respect to a fixed rate mortgage, the date on which
the principal balance of the mortgage, based solely on the
initial amortization schedule for that mortgage, and
irrespective of the outstanding balance for that mortgage on
that date, is first scheduled to reach 78 percent of the
original value of the property securing the loan;
A borrower can initiate cancellation after reaching the cancellation date (defined above as reaching 80%).
(a) Borrower cancellation
A requirement for private mortgage insurance in connection with a
residential mortgage transaction shall be canceled on the
cancellation date or any later date that the mortgagor fulfills all
of the requirements under paragraphs (1) through (4), if the
mortgagor -
(1) submits a request in writing to the servicer that
cancellation be initiated;
(2) has a good payment history with respect to the residential
mortgage;
(3) is current on the payments required by the terms of the
residential mortgage transaction; and
(4) has satisfied any requirement of the holder of the mortgage
(as of the date of a request under paragraph (1)) for -
(A) evidence (of a type established in advance and made known
to the mortgagor by the servicer promptly upon receipt of a
request under paragraph (1)) that the value of the property
securing the mortgage has not declined below the original value
of the property; and
(B) certification that the equity of the mortgagor in the
residence securing the mortgage is unencumbered by a
subordinate lien.
If the borrower doesn't go through cancellation, PMI gets terminated automatically upon reaching the above defined termination date.
(b) Automatic termination
A requirement for private mortgage insurance in connection with a
residential mortgage transaction shall terminate with respect to
payments for that mortgage insurance made by the mortgagor -
(1) on the termination date if, on that date, the mortgagor is
current on the payments required by the terms of the residential
mortgage transaction; or
(2) if the mortgagor is not current on the termination date, on
the first day of the first month beginning after the date that
the mortgagor becomes current on the payments required by the
terms of the residential mortgage transaction.
So that's the law for the standard case. There's a section excluding FHA and VA loans, a section excluding high-risk loans, and a section excluding lender-paid PMI. This law applies to loans made on or after July 29, 1999.