Untrue!

If you take a right turn out of that parking lot, the road winds up to Ocean View Drive, which runs right along bluffs overlooking the ocean. There are a bunch of national seashore beaches there which are worth checking out, and parking is free (I think) for bikes. If you continue up that way about a mile, you can take a left at Long Pond Rd, which winds down through the woods and crosses an overpass over Rt. 6, and right into Wellfleet town center without having to deal with the highway traffic. If you're really adventurous, you can look into the Saltonstall bikeway (of which the rail trail is a part) which runs north all the way to Provincetown.

I should also add that about 1/4 mile from the parking lot (on the left, towards rt. 6) is a little commercial area with a bakery called The Blue Willow which makes the best muffins I have ever had.

In terms of timing - the summer season is in full swing from June to August, meaning that the trail will be crowded during the day, and campgrounds/restaurants/etc. will be busy. If I were doing this, I'd aim for early September.