Apple may be right or wrong with their optimistic projections but people need to at least understand the business proposition they are offering. The concept of "making up the cost" has nothing to do with recovering the 3 free months from Apple as if it was a closed economic system. The idea is that the musician recovers the 3 free months from the entire music industry because Apple will have a wider audience and a bigger platform.
flawed model: get $0 for 3 months and never get it back whether the future Apple payments total $1 billion, $10 trillion, or infinity.
Apple's model: get $0 for 3 months but you (potentially) come ahead because we pay higher royalty AND we have the potential to convert a bigger % of 800 million iTunes accounts to paid streaming subscribers which will exceed Spotify's 20 million subscribers.
In other words, the artist is supposed to make business comparisons based on:
-- lost $$ for not being on Apple's platform and only providing music to Tidal & Spotify
-- more $$ from customers switching away from Spotify
-- more $$ from new streaming customers that would never have paid for Spotify but would subscribe to Apple Music because the app is already preloaded on the iPhone and there's less friction
(Each musician was supposed to weigh those bullet points to see if the big picture of skipping 3 months of payment made financial sense. It may or may not.)
As an analogy, it's as if a merchant concludes that accepting credit cards will "never make up the cost" because paying the monthly fees for the VISA/Mastercard mag swipe terminal and the transaction rates of 2% will never be paid back by the VISA/MC corporate entity. That's only true if one has a bizarre concept of thinking of the payment network as a closed system.
However, rational businessmen think outside of the CC payment system and conclude that accepting credit cards is net positive because behavior analysis shows that customers spend more when they can use a credit card instead of cash or checks.
 Thomas Baekdal's arithmetic and logic:
If we assume Apple Music will have $10 billion in revenue per year, we get this:
70% royalty / no free trail = $7 billion to artists
71.5% royalty / 3 months free = $5.4 billion to artists
After five years:
70% royalty / no free trail = $35 billion to artists
71.5% royalty / 3 months free = $33.9 billion to artists
After 10 years
70% royalty / no free trail = $70 billion to artists
71.5% royalty / 3 months free = $69.7 billion to artists
So, the artists never make up the cost while Apple saves
$1.6 billion the first year of Apple Music.*