Uh, you absolutely can, unless the account is locked. All the person who tweeted can do is delete the tweet.

You can embed any tweet anywhere you feel like (and actually the embed won't fully disappear when the tweet is deleted, but I digress).

This is somewhat of a legal gray area, but courts have ruled in the copyright owner's favor in a few cases like this (see https://tingenwilliams.com/2020/does-embedding-a-tweet-count...). If I post a picture on Twitter, sites other than Twitter aren't free to use it regardless of whether they are rehosting or embedding it.

Yea but if you embed it (e.g. iframe), then do you technically need permission? I would expect, and hope so, but it could be a grey area again.

If you are clamoring for a grey area, maybe just do the ethical thing and ask.

And yes, people have lost cases about using embeds too.

But does Shoutout ask the OP for permission to display the tweet? I've never heard this "you can't just pull tweets from the web.." twitter provides the embed capability, and doesn't mention anything in their terms (from what I can find) about asking for OP permission.

This strikes me as something that took longer to build as a service, than it would take an individual to build for their own app.

We don't ask for permissions. We believe in positive-sum game.

Social proof is given in the first place by people to people whose work or service made a positive impression on them.

We focus to showcase that and leave the rest.

I can understand feeling that way, and I would too. But you've signed over to Twitter the right for them to display your tweets in any way they see fit, and they've given everyone else permission to embed your tweets wherever they want (subject to some TOS no doubt).

You have signed over the right to Twitter, not random third parties. They are not using Twitter's embed API to render the content, but even if they did it wouldn't automatically absolve them from having to get permission. Plenty of courts have already ruled on this in the copyright owner's favor (specifically for Twitter and Instagram embeds in fact).

Agreed. Even if it's legal I'd be upset. I'd sever my relationship with the company and maybe post a negative review warning people not to post positive reviews.