It seems on the whole difficult to construct a theory that shall meet all the facts.

Perhaps a mixed hypothesis would be best.

It is probable that memory has been to some extent at work (the form of the quotation naturally suggests this) and is to account for some of Polycarp's variations; at the same time I cannot but think that there has been somewhere a written version different from our Gospels to which he and Clement have had access.
There are several other sayings which seem to belong to the Sermon on the Mount; thus in c.

vi, 'If we pray the Lord to forgive us we also ought to forgive' (cf.Matt.vi.14 sq.); in c.

viii, 'And if we suffer for His name let us glorify Him' (cf.Matt.v.11 sq.); in c.