In regards to access to services, a "provisional" diagnosis- if noted as such in the record- may be indistinguishable from no diagnosis, as far a some treatment funders are concerned. As to who can give an ASD diagnosis that would qualify the client for insurance (or state birth-to-three program) funded services, it is likely codified and differs from state to state. In my home state (MA), a diagnosis of ASD from a psychologist or physician is required. In CT, a diagnosis from a licensed social worker would qualify for birth-to-three services, but maybe not insurance.
As to the how, that is not as clear cut. Here's a definition from the MA Law (Act Relative to Insurance Coverage of Autism):
“Diagnosis of autism spectrum disorders”, medically necessary assessments, evaluations including neuropsychological evaluations, genetic testing or other tests to diagnose whether an individual has 1 of the autism spectrum disorders."
Pretty vague and, in the case of "genetic testing", not totally based on the science. In practice, if you are following DSM-5 criteria, the symptoms need to be present currently or by history, and must be present during the "early developmental period." The history part and early developmental period are not too much of an issue for me, as I'm only seeing really young kids and am usually getting history from multiple sources (e.g., parents, early intervention therapists, pediatricians). However, I do think it is good practice to differentially weight and give more importance diagnostically to the symptoms I actually observe. For example, if parents report an absence of pretend play skills, but the child comes to the office and spontaneously and consistently engages in multischeme play with a doll and representational toys that they have never seen before, I'm likely to conclude that they have pretend play skills. Similarly, if parent or teacher ratings on an SRS-2 indicate appropriately developed social interaction skills, yet the child does not make any eye contact, doesn't respond to his name, and doesn't use speech or communicative gestures for 2 straight hours, I'm going to more heavily weight what I saw.
You can see where this would be difficult as the clients get older and a) through therapy, maturation, etc. develop more subtle and consistent social interaction skills; and b) get farther removed from the "early developmental period" (and may not have a second source or data), self-report data may be the best you have for a lot of things. Additionally, there are many more other things that cause ASD like symptoms in adults, and differential diagnosis is much trickier than in a 2 year old (where I'm typically deciding between ASD, language disorder, global developmental delay, or intellectual disability- or a combination thereof). In practice, I use structure criterion- and norm-referenced tests to identify specific symptoms of ASD, identify/rule out pure language delays, and identify/rule out global developmental delays. Could i diagnosis accurately without these tests? Most likely I could at the extreme ends of things (e.g., high level of consistently symptoms of ASD or high level of consistent behaviors incompatible with an ASD diagnosis). It would be trickier for those kiddos in the middle. I actually get a lot of "second opinion" cases (both Dx and no-DX) from a local developmental pediatrician who meets with kids unstructured for 30 minutes and then gives (or doesn't) a dx.