If you check the headers, you will see that on api.twitter.com, the statuses/oembed endpoint is indeed subject to the default rate limit of 180 calls in 15 minutes, e.g.
-> "x-rate-limit-limit: 180\r\n"
-> "x-rate-limit-remaining: 176\r\n"
-> "x-rate-limit-reset: 1465549655\r\n"
If you’re still using that endpoint, but want to switch over, you should note that the format of the oEmbed response from the newer publish.twitter.com oembed endpoint is different.
I’m making a note that we should clarify the documentation around this recent change to the API.