Oh, right! We can be like those weird lamprey things that eat sharks! A huge alligator would make a decent host, and wonderful genetic material, assuming we can get a least a little bit by nomming on it. I mean, how's it gonna get us off, a back-scratcher?
Actually yes. Earth critters of this type are very smart and dangerous in a HUGE number of ways, but they are almost impossible for earth creatures of our size to harm, and they rarely eat things of our size, even when they could (think of plovers feeding from a crocodile's mouth - in case you didn't know about this and want to read of it
http://webecoist.momtastic.com/2009/03/01/symbiotic-bird-animal-relationships/).
Now, we're not going to be a little friend - and this log may have grown to its size from eating sewer mice, so it may VERY much think of something our size as a normal meal.
Typical crocy defenses include very fast rolls that DO scrape against the surroundings if there's anything close, often while lashing it's tail and occasionally flinging a limb at odd moments. I -hope- we can cling as if attached, and if not, that our many limbs help.... but I'd rather not upset the critter at all until we're (safely?) inside. I devotely hope that if we can actually get inside its body there will be absolutely nothing it can do to save itself. I'd be thrilled for us slip in between two of its teeth and lodge in its throat, I'd be delighted if we slide into a nostril, and I'd not be disturbed at all if we managed to enter its cloaca. Note that it may well have parasites already. If so, it may be wise for us to keep a watch for them as we feed.
It'll probably get us off by drowning us. We have lungs so water is probably not a good place to live.
Ahh, do we have lungs? Could you quote where we were told we did, or where we were told that we breathed through any means?