I worked for a company that did something similar (and is mentioned elsewhere in these threads). We a/b tested it, and just from the metrics, getting someone to download the app was so valuable from a stickiness perspective that it _looked_ like it was worth the negative effects.
You're right though, from a user trust perspective it's pretty horrendous. Regardless of whether that was measurable or not, there are things that are just so infuriating to users that you shouldn't do them. I'd argue the cost in terms of internal morale and employees' trust that we're doing the right thing for our users, and their sense of pride in their work, way more than offset any metrics gains.