This is normal.
The GPS internal trip statistics are computed from the 1/sec locations and BaseCamp only sees the tracklog (which is a subset of the 1/sec locations). It is a trivial mathematical proof (using the triangle inequality) to show that the distance computed from the tracklog must be less than or equal to the distance computed from the 1/sec positions. (The 60 series and the 62 series tracklogs are limited to 10K points so the tracklog can only store 2.7 hrs of 1/sec data and thus one usually records points less often.)
Any "fix" to BaseCamp would actually produce an incorrect result given the data that it sees. (I presume that a "fix" would be to multiply the computed distance by a fudge factor slightly greater than 1. You can look at your past trip data and estimate an average fudge factor yourself. Unlike a Garmin-supplied fix, you will at least know what you have done to your data. Note: the fudge factor will depend upon the track recording method and frequency. (main menu>setup>tracks>{record method, recording interval}. FWIW, I generally use Auto, Normal (the default).)
BTW, the difference that you observe in the above example is a bit larger than I usually observe, but it will vary from trip to trip and, as noted above, also depends on the recording method and interval.
Doug