sanchin of goju ryu and uechi ryu is descended from white crane sanzhan.
our san he chien is not exactly the same form, but it has similarities. The closest to our form I've seen is the wuzhu quan/five ancestors fist version, which also shares roots with the southern white crane styles, I believe.
Here are two white crane versions, the uechi ryu and goju ryu versions of sanchin
http://www.youtube.com/watch?v=mWh-uhw4C9s
five ancestors version
http://www.youtube.com/watch?v=Yla9j0AangU
note how the second crane form and the five ancestors have attack sequences at the end similar to our form. The five ancestors hand postures are most similar to ours, I feel.
Also, the characters GM The used for san he chien mean "three harmonies fist", while san zhan means "three battles". What the significance of that is we'll have to guess, but it certainly is a relative of sanchin/sanzhan.
In terms of there being tiger in goju ryu, I did read somwhere that Chojun Miyagi had a Chinese friend or acquaintance on Okinawa who taught a tiger style. I don't remember where or what the name was. This doesn't mean that this fellow's tiger style was a major contributor to goju ryu, but Miyagi did a lot of traveling and studying with different people on Okinawa and in China, on top of his learning from Higashionna. Patrick McCarthy even mentions that he studied at Chin Woo in Shanghai sometime in 1936. What exactly he learned from where and how it influenced the karate he taught, I think no one will ever know. The primary art he taught, and most of the kata, did come from Higashionna.
Now Uechi ryu is a different matter. Although it's main kata are also found in goju ryu, the founder of Uechi ryu said that the style he learned in China was based on the principles of the crane, tiger, and dragon. He supposedly learned from a completely different teacher than Higashionna (and at a much later date). The kata are performed a bit differently, as is seen with the sanchin kata.
So it may not be a solid link such as there is with the white crane teacher that taught Higashionna, I wouldn't say it is impossible that some tiger elements made their way into the naha te kata.
Pretty much all the karate styles, naha te and especially shuri te, don't have any good record of who or where the art came from before it got to Okinawa, except for oral tradition and legend. Shorin ryu/shuri te kata were mostly formed in the late 18th and early 19th century, vs. the naha te/goju ryu which had it's Chinese connection in the later 19th century, so the facts on these styles are slightly more available. A lot of the shuri kata are said to have been taught by random Chinese envoys/bodyguards and stranded sailors whos names are only preserved in the kata name, like "wanshu", "chinto" and "kusanku". So not having information after a certain point is common, no matter what style it is.
There is definately tiger in our style. I have started to wonder if a bit of indigenous silat might have got into our style, too. I used to assume it is just shaolin ditang, but after seeing some silat demonstrations with a lot of low to the ground rolling and kicking ground techniques, I wonder if that's where our brown belt crane forms get their strange mix of southern white crane-style techniques with the sanchin stance and the "broken leg" stance and ground techniques which I always thought were a little strange together.