Why was Duke Frederick suspicious of Rosalind in Act I, scene iii of As You Like It, and what is meant by "as innocent as grace."

The clue to understanding Duke Frederick's suspicions and
banishment of Rosalind lies in the preceding scene, Act I, scene ii. The last half of
the scene is devoted to the wrestling match between Orlando and the challenger Charles.
Several things are revealed at this wrestling match. First of all, it is important to
bear in mind that Duke Frederick is there and standing near to Celia and Rosalind since
he directs remarks to them. It stands to reason that he can also readily hear what they
say and wittiness what they do.

Let's start with what is revealed
because of Rosalind and Celia. At the Duke's bidding, Celia and Rosalind attempt to
dissuade Orlando from wrestling. His responses make the girls admire his courage and
manliness. The result is that they cheer him on. When he wins, Rosalind's emotions go a
step beyond admiration and turn to the beginnings of love. This is attested by her gift
to him of her necklace.

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ROSALIND
Gentleman,
Giving
him a chain from her neck
Wear this for me, one out of suits with
fortune,
That could give more, but that her hand lacks
means.

With the Duke's
vantage point, he sees all and notices that Rosalind is poised to fall in love with
Orlando. This knowledge will be important following other
developments.

Next, let's look at what is revealed after Orlando wins
the match against Charles. The Duke is not displeased that Orlando has won but is
greatly displeased to find out that Orlando is the son of Sir Rowland de Boys, because
de Boys was an enemy of Frederick:

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DUKE FREDERICK
I would thou hadst been
son to some man else:
The world esteem'd thy father honourable,
But
I did find him still mine enemy:
Thou shouldst have better pleased me with
this deed,
Hadst thou descended from another house.
But fare thee
well; thou art a gallant youth:
I would thou hadst told me of another
father.

With these
revelations in mind, it suddenly becomes clear why Duke Frederick is suspicious and
banishes Rosalind in Act I, scene iii, accusing her of being a "traitor" and
sarcastically saying all traitors are "as innocent as grace itself" when what he means
is that their innocence is a falsehood, a disguise for their treachery. We now see that
Frederick is suspicious of Rosalind because she is the daughter of his enemy--the
brother whom he deposed from the throne--and she is potentially poised for an alliance
of marriage with the son of another enemy, Rowland de Boys. Duke Frederick fears an
alliance of his enemies who might plot his overthrow and the restitution of the crown to
the rightful wearer, Duke Senior, who is Rosalind's father and Orlando's father's
friend. Of course, Frederick would not want to say this and thereby possibly put
treacherous ideas in Rosalind's thoughts.