偶然: a chance meeting and an explanation of similarity
Read an unexpected meeting with an old friend against the claim that two works' similarity is mere coincidence, distinguishing event and explanation.
An unexpected meeting while traveling
旅先で昔の友人に偶然会いました。 reports happening to meet an old friend while traveling. 偶然, read ぐうぜん, describes the chance nature of the actual meeting with 会いました.
The travel setting and old friend are supplied. Do not change the encounter into a prior appointment or add an ongoing relationship after the meeting.
Similarity described as mere coincidence
二つの作品が似ているのは単なる偶然だ。 explains the similarity between two works as mere coincidence. 単なる偶然だ describes that similarity; it does not report meeting a person.
Read both the similarity and its description as coincidence. The sentence does not establish that the works share an author or that one copied the other.
An event and an explanation
In the first, 偶然 modifies meeting. In the second, it names coincidence as the explanation of similarity. The word's event and explanatory roles differ.
The question is not about choosing the spelling for meeting. It concerns the unexpected nature of the encounter and the explanation applied to similar works.
Does 単なる偶然 in the two-works example report a chance meeting?
Show the answer and why
No. It describes their similarity as mere coincidence. That explanatory role differs from unexpectedly meeting the old friend while traveling.