The cross domain policy for search.twitter.com permissive:
<cross-domain-policy>
<allow-access-from domain="*" />
</cross-domain-policy>
And for api.twitter.com it's quite restrictive:
<cross-domain-policy xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="http://www.adobe.com/xml/schemas/PolicyFile.xsd">
<allow-access-from domain="twitter.com" />
<allow-access-from domain="api.twitter.com" />
<allow-access-from domain="search.twitter.com" />
<allow-access-from domain="static.twitter.com" />
<site-control permitted-cross-domain-policies="master-only"/>
<allow-http-request-headers-from domain="*.twitter.com" headers="*" secure="true"/>
</cross-domain-policy>
meaning that the only way to talk to api.twitter.com would be to call a script on your server and then proxy the request to twitter.