It would appear that LeCroy follow Agilent/Keysight in this respect (or, at least, Tektronix's presentation of what Agilent's method is). This can be seen from their probe manuals, for example for the ZS4000 active (single-ended) probe. They provide the probe impedance as a function of frequency and advocate that the user corrects for it when interpreting the measurement, using the formula:
$$V_\mathrm{out} = Z_\mathrm{probe}/(Z_\mathrm{probe}+Z_\mathrm{source}) \times V_\mathrm{in}$$
I avoid quoting further from their manual to avoid potential copyright issues (because it would require the whole section to be quoted to reproduce it properly here), but if you follow the link and read the manual, you will find that everything is quite clearly stated.
For the differential probes operating in the 10 GHz range (for example, the WaveLink D1030), their approach is slightly different to either of the ones presented in the Tektronix technical brief. The probes measure the loaded signal, as per Agilent, but they provide equalization software (Virtual Probe) to recover the unloaded signal. One models the circuit impedances and indicates the type and location of the probe, and the de-embedding is done accordingly. They summarize it as follows (quoting from the WaveLink probe manual):
Teledyne LeCroy probes are calibrated at the factory using a Vector Network Analyzer (VNA) to measure a system (probe plus test fixture) frequency response. The test fixture is de-embedded from the measurement using Teledyne LeCroy's Eye Doctor tools so the remaining frequency response is due to the combination of the test signal and the probe loading on the test circuit. The system frequency response is then calculated for these remaining circuit elements.
If you wish to de-embed the effect of probe loading on your circuit, you can use the appropriate equivalent circuit model ... and Teledyne LeCroy's Eye Doctor tools to accomplish this.
You can also use Teledyne LeCroy’s Virtual Probe option. This option allows you to select the probe tip from a list of supported tips. Your selection applies a corresponding s-parameter file that is derived from the equivalent circuit model of the tip.
However, I haven't actually used these probes, so I can't comment on how good the software is.
Your college does not seem to remember her statistics lessons. The additional higher frequency noise can be trivially filtered with a low pass filter, and the filtered signal might be better than one sampled at low frequency (oversampling).
Note that using a standard oscilloscope to record live ECG violates patient protection, as medical equipment requires better electrical isolation than those devices usually provide.
Best Answer
When an oscilloscope says it has a 50 MHz bandwidth, that usually means the frequency response is 3dB down (half the power or 71% of the voltage) at 50 MHz.
Although Nyquist says you only need to sample at >100 MHz to reproduce a signal with a 50 MHz bandwidth, that means a signal with no energy above 50 MHz. The usual definition of 3dB down leaves plenty of energy above that.
Sampling at 1 GS/s, we would like no energy above 500 MHz. I'm sure our 50 MHz 'scope could achieve that filtering comfortably, if it wanted to. It probably achieves it accidentally, at least in cheaper 'scopes, by only designing the amplifiers for 50 MHz and letting them roll off at higher frequencies.
By default, most oscilloscopes connect the sampled dots together with straight lines. A 20:1 ratio between the frequency of the displayed waveform and the sample rate is just about enough to get a good-looking sinewave.
The bandwidth limitation on a 'scope probe is a similar beast to that of a scope, it should work up to that frequency, and you don't know what's going to happen above that. Don't assume either a scope or a probe is going to implement a proper filter above its bandwidth specification, don't assume it's going to work to specification above it.