For ease of reference, let's give names to your experiments:
Experiment 1:
- Data: recordings of a few sample syllables. For the sake of argument, let's assume the syllables are canonical recordings, and you've avoided nontonal pitch transformations such as prosody, downstep etc.
- Data: the information: "this is an HL language".
- Expected result: I can identify the HL tones.
Experiment 2:
- Data: recordings of a few sample syllables as above.
- Result: I cannot identify whether the language is tonal, nor whether the tones are high or medium or rising etc.
Does experiment 1 necessarily succeeds?
Assume a language A with the following tone sandhi rules, where each letter stands for the pitch of a single syllable:
- /H#/ → [H]
- /L#/ → [L]
- /HH/ → [RH] (raises to high)
- /LL/ → [FL] (falls to low)
- /HHH/ → [LRH]
- /LLL/ → [HFL]
[L] can be either /L/ or /H/, depending on its position. If you just give me isolated syllables, I can't know the phonemic tone. (Many other phonetic transformations could be imagined; perhaps /H/ tones end up lower-pitched than /L/ tones when the /H/ is between nasals and the /L/ follows an aspirate, etc.)
But let's say you're not worried about contextual tone phonetics like that. You want to know about good standard canonical cases where high tones are higher in pitch, dammit. So we do a modified experiment 1':
- Data: recordings of a few sample syllables. These are the canonical-est realizations of each tone, not subject to any sort of phonetic or contextual transformation.
- Data: the information: "this is an HL language".
Now I can identify the high-tone syllables—but that's a trivial result, because I've been told what to find (I know that the language is tonal, that its tones are distinguished by high and low pitch, and that they're not subject to pitch changes). Experiment 1' amounts to giving me the territory and the map; of course I can find stuff on it, but that tells us nothing about universals. For example, if I tried to infer an universal from it, I might wrongly conclude that /H/ tones are always realized higher in pitch than /L/ tones, even in a world where languages like language A exists.
Does experiment 2 show that languages have something specific in the phonetic realization of tones?
Assume for the sake of argument a restricted universe where all tonal languages realize tone in exactly the same way: /H/ is always a simple level high-pitch, and /L/ is always a simple level low-pitch.
Let's postulate a non-tonal language, say language B, with the following phonetic behavior: aspirated consonants cause high-falling pitch, unaspirated stops cause medium-level pitch, and voiced consonants cause low-rising pitch, except that the first syllable of a word is always low-rising. From this data, I can't even tell whether B is tonal or not; from my point of view, pitch seems to be all over the place. And yet, in this universe, every single tonal language has exactly the same phonetic realization of tones.
So the answer is again no; I can't conclude anything about tone universals (or lack thereof) from experiment 2.
As an aside, it's worth noting that in the real world, tone is not just pitch.