Trump just asked his audience:

[Ms. Toad]

11. I'm not sure there has to be acceptance after a conviction.

because once there is a conviction, the individual is already legally guilty.

The Burdick case was pre-conviction, and the court was trying to force him to testify against his will, in a manner that would have incriminated himself but for the pre-conviction pardon. He wanted to plead the 5th, remain silent, and retain the possibility of maintaining legal innocence. The court said - pre-conviction - that he was not obligated to accept the pardon (and the implication of guilt that goes with it). That horse is out of the barn for Arpaio. He's already legally guilty.

The application for a pardon doesn't require admission of guilt, although taking responsibility for the offense is strongly encouraged:

In addition, you should bear in mind that a presidential pardon is ordinarily a sign of forgiveness and is granted in recognition of the applicant's acceptance of responsibility for the crime and established good conduct for a significant period of time after conviction or release from confinement. A pardon is not a sign of vindication and does not connote or establish innocence. For that reason, when considering the merits of a pardon petition, pardon officials take into account the petitioner's acceptance of responsibility, remorse, and atonement for the offense.

https://www.justice.gov/pardon/file/960581/download

I can't imagine a spontaneous pardon requring a stronger admission of guilt than the petitioned for pardon.