How precise is the Fibonacci distances trick?

tables.txt

km | mi (est.) | mi (act.) | error
-----------------------------------
 1 |  1        |  0.62     |  60.9%
 2 |  1        |  1.24     | -19.5%
 3 |  2        |  1.86     |   7.3%
 5 |  3        |  3.11     |  -3.4%
 8 |  5        |  4.97     |   0.6%
13 |  8        |  8.08     |  -1.0%
21 | 13        | 13.05     |  -0.4%
34 | 21        | 21.13     |  -0.6%
55 | 34        | 34.18     |  -0.5%
89 | 55        | 55.30     |  -0.5%

mi | km (est.) | km (act.) | error
----------------------------------
 1 |  2        |   1.61    | 24.3%
 2 |  3        |   3.22    | -6.8%
 3 |  5        |   4.83    |  3.6%
 5 |  8        |   8.05    | -0.6%
 8 | 13        |  12.87    |  1.0%
13 | 21        |  20.92    |  0.4%
21 | 34        |  33.80    |  0.6%
34 | 55        |  54.72    |  0.5%
55 | 89        |  88.51    |  0.5%
89 | 144       | 143.23    |  0.5%