@Edgington Hi, this is probably because of different calculation of both values.
Cloud base is directly taken from ECMWF parameter called "ceiling". It is height (above model orography i.e. AGL) of cloud layer covering more than 50% of the sky. It estimates height where you can expect "significant clouds". Detailed description is here: https://confluence.ecmwf.int/display/FCST/43r1+new+parameters%3A+Ceiling
On the other side the grey meteogram is calculated from relative humidity. It can be explained as a distribution of water in the atmosphere. The height in the meteogram is in pressure levels. km/ft values are only rough estimation and they are AMSL. I admit that this can be confusing.
Possible explanation of the difference: There could be signigicant humidity (almost 100%), so there are drawn clouds in meteogram, but the cloud coverage according to ECMWF is less than 50%, so the ceiling is considered to be higher.
In such strange case it is better to look also in cloud maps, which can give you better overview. However, if the location is in the mountains then the values can be misleading, because model orography is very rough.