Yes, the use of "is" in this quotation is grammatically correct. Compare the well-known example "It is I/me", where people argue about whether to use "I" or "me", but never about whether to use "is" or "am". A verb agrees with its subject: the subject here is "the reason", which is singular. In modern English, only pronouns (like I, you, or in relative clauses who) can trigger first-person or second-person agreement on an associated verb. Because "the reason" is not a pronoun, it has to trigger third-person agreement. So it is correct to use the third-person singular form.