Looking at the examples in the paper linked above, of Japanese sentences purportedly showing "dative subjects" (page 8 in the PDF), I note that the nouns marked by に in the Japanese are only subjects after translating into English.
For verbs in the potential, much as in passive constructions, the に in these sentences marks the agent, not the subject.
Compare:
- Passive: 「彼に英語が話される」 → "English is spoken by him."
- Potential: 「彼に英語が話せる」 → "English is speakable by him."
In both sentences, the verbs are intransitive, 英語 is the subject of those intransitive verbs, and 彼 is marked as the agent of the actions.
Notably, intransitive verbs of potential that are derived from transitive verbs, like 話【はな】せる above, still semantically describe an action happening upon something, where that something is not the agent -- this is different from a "regular" intransitive verb, which semantically does not happen upon something, but instead describes an action occurring by means of that something itself.
More here in an older answer post, regarding the development and semantics of Japanese potential verbs.
In like fashion, the verbs わかる and できる mark the subjects with が and the agents with に. While not derived from transitive verbs, they function grammatically and semantically in a similar way -- they describe a quality of the subject, as something that is "do-able by" an agent marked with に.
The author of the linked paper Case Patterns is one Ellen Woolford, who appears to be this person. She specializes in syntax, but doesn't seem to have any particular familiarity with Japanese itself.
In the linked paper, she pulls the Japanese examples of purported "dative subjects" from Masayoshi Shibatani's 1977 work Grammatical Relations and Surface Cases, available here via JSTOR (free registration required). Shibatani goes in quite deeply, and his work is rife with abbreviations that make it quite difficult to read for non-specialists. That said, his analysis from page 799 (referenced by Woolford's paper) consistently describes subjects marked by に and objects marked by が, for sentences using verbs that Japanese-language references consistently describe as 自動詞 or "intransitive verbs" that take no objects -- verbs that only become "transitive" after translating into the common English glosses, verbs like intransitive ある translated as the transitive "to have".
Reading a bit further in Shibatani on pages 800-801, he makes a complicated argument about "subject"-ness based on how reflexive (using 「自分」) and honorific constructions focus on the noun marked with に. I posit that construing this as "subject-ness" is a mistake -- this indicates not that the に-marked nouns are subjects, but rather that the agents in such constructions have a higher primacy of focus for reflexives or honorifics than do the grammatical が-marked subjects of the intransitive verbs.
Re-casting this as "dative subject" and "nominative object" for verb constructions like ある is a strange stretch. Many languages use intransitive constructions not dissimilar to Japanese ある ("there exists") to express that someone "has" something. Compare:
- JA: 彼には家がある → "by him, there is a house" → "he has a house"
- HU: [nek]{に}[i]{彼} [ház]{家}[a]{POS} [van]{ある} → "by him/her, a [third-person singular possessor] house there is" → "s/he has a house"
- NV: [kin]{家} [bee]{彼に} [hólǫ́]{ある} → "a house by him/her there is" → "s/he has a house"
In each case, the verb is simply a marker that something exists -- this is not transitive in any of these languages, and the statement only manifests any transitivity after translation into idiomatic English using the transitive verb "have". Claiming the existence of a "dative subject" and "nominative object" violates the principle of Occam's razor, and does much to muddy the waters.