The iOS app would've been developed in partnership and with the blessing of Google (aka Co that owns YouTube).
Microsoft had no such relationship with Google and instead chose to release their own unofficial YouTube app (first without ads) clearly violating the YouTube API TOS. Knowingly breaking the law and expecting a favorable outcome reminds me of "Queue Jumpers" who illegally enter Australia, they're not legally allowed to enter, but they continue to do so because the outcome is more favorable to their lively-hood when they do.
So Google blocks Microsoft, who wants to turn this into a anti-Google PR stunt and is openly crying foul trying to rally public support for their plight since they have no legal recourse.
Which is odd for Microsoft who loves exploiting the legal system to others detriment. I'm honestly shocked that Google isn't bending over backwards to help a competitor who is actively extorting the Android ecosystem through patent litigation (on tech created by Google), who makes more money on Android sales than even Google does (who has contributed significant resources into making Android).