However both diamonds and bitcoin receive their scarcity from being in the hands of relatively few people which purposefully control the market to give them higher value.
Wrong. Bitcoins are scarce (not infinite) because the algorithm to create Bitcoins (generation subsidy) tends toward zero and is published (open source).
Diamonds are not truly scarce, since they can be synthesized at or near the cost of mining them naturally.
Why are you people always nitpicking on the sematics?
Bitcoins are tightly controlled by the upper 1% of participants with a total percentage ever sold on the market (also equals spending in current paradigm) of 3%.
97% of all bitcoins are hoarded period.
Again, other details are just semantics not really relevant to the analogy.