Of course our scholars have already discussed these types of issues in classical fiqh works. The Hanafis do not allow tawaf to be done by the one who is physically fit except while walking. Most of the Shafi'is and Hanbalis allow riding/sitting/being pushed even if the person is physically fit (since it is authentically narrated that the Prophet (SAW) did tawaf on his camel once). And the Malikis say that for an obligatory tawaf, the one physically fit must walk, while for a nafl tawaf, s/he may ride or be pushed.
Of course, ALL agree that the one who is weak or otherwise unable to walk may instead ride or be pushed in a wheelchair.
Regardless of the fiqh involved, I'm sure the guy got a quick, easy tawaf done and had plenty of comments/stares along the way!
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