To provide some citations from academic papers rather than news articles:
The Rights and Wrongs of Prostitution 09 January 2009
Hypatia: A Journal of Feminist Philosophy
This division already exists in the Netherlands where “sex surrogates” who work with disabled people are legally and socially constructed as different from prostitutes who work with able‐bodied clients.
Sex rights for the disabled? Journal of Medical Ethics 2010;36:152-154.
Several European nations, including Germany, The Netherlands, Denmark and Switzerland, allow limited ‘touching’ services for the severely disabled through non-profit organisations.6 Nina de Vries, a Dutch-trained therapist based in Berlin, has been offering such services to patients with Down's syndrome, autism and severe brain damage since 1997, including to individuals incapable of speech or complex communication. (She describes herself as a sexual assistant, or Sexualbegleiterin, but does not reject the term prostitute.) Despite considerable demand for such ‘massages’, these services remain entirely privately funded.
This seems to be at odds with the news articles but I trust academic papers more.
The Guardian article cites another article that talks about a Holland "style" scheme but doesn't specifically point to a holland government source. As best I can tell that seems to be based on tabloid articles that interpret the monthly disability allowance (which you can spend on anything, including prostitutes) as monthly payments for prostitutes.
The Dutch government only legalized prostitution in 2000 so the 1992 New York Times article seems odd. I can't find any other details of the case and the origional article is no longer on the NYT site.
It seems plausible it could be a poor translation or something less dramatic like the municipality not being allowed to control what disabled people spend their stipend on if they were trying to refuse it because it was going to be spent on prostitutes.
The Surprising Way the Netherlands Is Helping Its Disabled Have Sex
While there is no direct "sex grant" per se, the benefits citizens with disabilities receive can be spent however they like. Some reports indicate that they can use these benefits to access sex services 12 times a year, but information on the specifics is elusive.