Wikipedia on Automixis says:
"Some authors consider all forms of automixis sexual as they involve recombination. Many others classify the endomitotic variants as asexual and consider the resulting embryos parthenogenetic."
From the last words of this difficult statement it may reversely be infered that parthenogenesis is defined as non-sexual. There do exist different definitions of "sexual reproduction". What some authors consider non-sexual and parthenogenetic, others consider as sexual and: non-parthenogenetic. All agree on the term parthenogenetic denoting a-sexual reproduction.
However, it also results from Wikipedia that in the context of parthenogenesis, the existence of haploid gametes, contrary to common definition, is not a prerequisite of sexual reproduction, as with all forms of automixis haploid gametes are not involved.
As the question seems to assume there are different opinions on some forms of automixis being sexual, thus parthenogenetic, or not.
To easen up: you must look at the action - what looks like parthenogenesis maybe is not sexual, opinion diverge
Automixis may loosely be used as a synonym for parthenogenesis process and vice versa, the more if parthenogenesis is seen as the opposite of any mating form of reproduction that uses gametes (or is hermaphroditic). As far as some authors consider automixis that mitotically produces a stage of haploid cells as sexual reproduction, thus non-parthenogenetic they are looked upon by other authors who do not share that definition as speaking of "sexual parthenogenesis". Some kind of rebuff, I think, as no author defines parthenogenesis as sexual.
Some say that forms of automixis that involve some kind of - haploid - "gametes" (think of haploid cells as the first stage of a developement of gametes) should not be considered parthenogenesis, but sexual reproduction.
Conversely, automixis and the crossing-over of genes is not a sufficent condition for defining those processes as sexual, thus non-parthenogenetic. All agree that "mixis" alone is no reason to categorize the specific process as non-parthenogenetic.
To easen up:
Standard, normal, processes of parthenogenesis do not imply the recombination of genomes, and are termed non-sexual without discussion (which might come to a surprise and is nothing trivial either, and that might have been one reason to put the question).
Quote from your question: "The ones that say (parthenogenesis is) a form of sexual reproduction,they focus on the fact that meios has happened in the process..." That denotes the very point where different opinions come together. To easen up: The ones that say so do not intend to define those "meiotic"/crossing over forms of reproduction as parthenogenic. On the contrary (this is intricate, sorry for being clumsy or "not learned") they want those forms to be counted out. Counter-intuitively, those authors do not see those processes as parthenogenic (without considering them as hermaaphroditic). So there is sexual reproduction with no gametes as cells that have had some life, different lives.
As it occurs only now: those who consider the production of "tiny" haploid cells as sufficient to render the process sexual in charakter, their point of view can easily be reconciled with a more general, common, definition of sexual reproduction that is based on the use of gametes; the concept of gametes is expanded on those haploid "endomitotic" cells that instantenously fuse and are derived from one and the same individual (as it may occur now: the character is hermaphroditic, then!)
You may find that irritating frame shift in the very first sentence of Wikipedia (to my mind the following quote might have been incited your question):
Wikipedia: "Automixis[...] is the fusion of (typically haploid) nuclei or gametes derived from the same individual.[...] The term covers several reproductive mechanisms, some of which are parthenogenetic." They should not say "are" (parthenogenetic).
