While I agree with you that the burial clothes COULD have been paid for by a wealthy patron, Occam's Razor suggests that another explanation is much more likely.
Historian Philip Harland note the lack of Christian memorial momuments of the type that well-to-do people often had in the first 2 centuries of the Christian era, and also has this to say:
"..There is truth in [Celsus'] observation, about a century after Paul, that attachments through workshops of wool-workers, shoe-makers, and clothing-cleaners continued as a key resource for newcomers to some Christian groups (Origen, Cels. 3.55)."
http://www.philipharland.com/articlehandbook17.html
Harland also notes the role of wealthier members of the congregation as benfactors.