I'll start by saying this. I don't agree with the statement; however, I can defend the statement and provide evidence.
"The Merchant of Venice" is a great comedy, because it strikes a wonderful balance of comedy, romance, and true love. Reading it or watching it is like watching a modern day great romantic comedy. "The Merchant of Venice" deserves to be grouped with other great romantic comedies such as "The Princess Bride," "Pretty Woman," and "Say Anything."
Being a romantic comedy, "The Merchant of Venice" has wonderful displays of love and romance throughout. Bassanio is so in love with Portia that he is willing to "risk it all" for a chance to win her affections (how very "Bacheloresque" of him). In order to do this he must humble himself and ask for money from his best friend, which is a difficult thing to do. "The Merchant of Venice" further ramps up the romance levels by having Jessica and Lorenzo run away together to get married. What's more romantic than a forbidden love?
But the play is more than just a bunch of couples wanting to spend some quality time together. The play is focused on the characters love and life long commitment to each other. That's why marriage is such a central focus of the play.
None of the above is comedy focused though. The love and romance is simply a device that Shakespeare uses to wrap his comedy around. "The Merchant of Venice" has it all when it comes to comedy. It has the token "funny guy" in Lancelot. It has twists and turns of relationships and mishaps. To top it all off, it has cross dressing. Even Hollywood banks on comedic cross dressing to get people into theaters. "Mrs. Doubtfire," "Tootsie," "The Birdcage," and "Some Like it Hot" are all examples of movies that had main protagonists cross dress. Those movies were not box office busts. Instead they were box office smashes that further launched acting careers. Shakespeare knew it was funny 400 years ago.
A final reason as to why "The Merchant of Venice" is such an effective comedy is because it is dark in places. Shylock is an evil character, and his "pound of flesh" deal is quite sinister. What these very low, dark sections do is further deepen the polarity between them and the comedic sections. The comedy sections are genuinely funny, but they are hilarious when compared to some of the play's darker elements.
To learn more about Elizabethan comedy and Shakespeare's use of comedy, check out this video: